The expansionist tendencies of Charles VIII toward Italy, especially Naples could be linked to his childhood seeing his father inherit the rich duchies of Anjou and Provence after Charles IV's death, more likely to Charles VIII it was the ambitious Burgundians that drove his ambitions southward. The loss of such a rich county as Champagne would pressure Charles to march south and claim a far richer and more prosperous land, the Kingdom of Naples. In 1481, the death of Charles IV of Anjou, passed the claim to the kingdom of Naples as the disputed heir of Joanna II of Naples. However due to Louis XI's passing and the fact that Charles IV never actually invaded Naples in his lifetime, this claim was quite weak, unfortunately an ace in the hole in the form of a death and a pope would occur.
Ferrante I of Naples was by all extents an incredible monarch, being able to establish a firm independent Naples away from Aragon and away from the ever powerful pope. This careful foreign and domestic policy would be standard of Italy throughout the 1470s and 1480s while alliances were formed increasingly with outside powers, they would never directly intervene in Italian affairs, this centralized style of foreign policy would be further displayed in the war of Ferrara between Venice and the various Italian powers wishing to limit Venetian growth in Italy, while various Italian powers were involved in the war such as Naples, the Papacy and Venice. Importantly no foreign powers were intervening, Burgundy's alliance with Naples was not triggered nor did this war trigger the ire of Aragon, or the Emperor. This fragile idea of an Italian centric foreign policy ironically shown by Ferrante I of Naples would immediately break upon his death.
The succession of Ferrante I of Naples would leave Naples in an incredibly strong position militarily and diplomatically but cash strapped. The papacy who still had great power over Naples demanded the traditional papal fief tax for the succession for Alfonso II who was his heir. However, Alfonso would refuse the fief tax due to the crown being cash strapped and the papacy would invite once again Charles VIII to take the throne. Already in 1489, Pope Innocent VIII excommunicated the old King Ferrante I of Naples over the feudal relation with Naples and invited Charles VIII to take the throne of Naples however the turbulent and yet balanced regency of France would forbid any attempt at invading Naples as Philip the Rich would continue his alliance with the Neapolitans that was formed at the time of Charles the Absolute who wanted Naples as a counterbalance against Milan, France's strongest ally in Italy at the time.
The death of Louis XI would not fundamentally change Burgundian policy towards Italy during this time, already under Charles the Absolute, Burgundy had practically all of Italy under their thumb, with Savoy a practical vassal, Milan a new Burgundian ally, Venice seeking to not alter the balance a reluctant Burgundian ally, the papacy favouring the Burgundians over the French ever since the pragmatic sanction of Bourges. Importantly for Burgundy was the alliance with Naples, which formed the basis of Ferrante's policy as Burgundy was far away from Naples and had no interest in the kingdom of Naples and willing to stop any strong power controlling Italy such as France and the newly formed Spain. The drift of Milan towards France rather than Burgundy would begin under the reign of Ludovico Sforza as regent. Ludovico would reverse the policy of alignment towards Burgundy as he saw Savoy fall into de facto vassalage and seeing France regather its strength. Ludovico would invite Charles VIII to help secure his regency against the Neapolitans.
Isabella who was the daughter of the king Alfonso II of Naples and was the one woman who opposed Ludovico's regency and perhaps her strongest ally and could counter France was Burgundy, unfortunately circumstances would befall upon the Burgundians as the peace of 1491 in the treaty of Dijon signed away a truce that would last until 1496, which forbid Burgundy from directly intervening in Neapolitan interests while the double crowned king, Maximilian would side with Ludovico seeking to bring a new imperial ally into Italy and strengthen imperial presence in the "shadow kingdom" that is Italy. This usurpation of Milan by Ludovico with both imperial and French backing would spell the end of the short reign that was Alfonso II of Naples.
The grand Burgundian-Italian alliance was co-opted by Charles VIII as he would march south to Naples with the full support of Milan and Venice, both Burgundian allies. The papacy who hoped to weaken the powerful kingdom opened Rome to Charles with open arms and he would march south to Italy. The extended war of the roses would lead John II to pursue neutrality as the reluctant withdrawal support of Charles VIII to a pretender would force him to declare neutrality, Burgundy already tied up with the peace at Dijon would reluctantly watch in horror as French forces under Charles VIII would stomp all over Italy. Aragon who was perhaps a permanent rival of France was bought with peace by reselling the lands Louis XI seized from Aragon due to a loan that was never paid by the Aragonese. Florence who was a French ally at the time would rise up against Charles VIII only to be crushed immediately by the French army.
Charles VIII's army was possibly the strongest army of France since the time of Charles VII, the defeat of the Swiss in Grandson by Charles the Absolute would shift Louis' military tactics as he observed the Burgundians co-opt the Swiss pike tactics and improved them significantly to absolutely annihilate the Swiss. These reforms under Louis XI would be accelerated by Charles VIII who lead this incredibly powerful French army to demolish Italian armies and fortresses. This string of victories in Milan, Florence, Rome and Naples would end with Charles VIII who was proclaimed King of Naples in February 1495. This rapid conquest would create the formation of the league of Venice and while Burgundy would not join it immediately Aragon and the Holy Roman Empire would. Burgundy at this point was itching to join the conflict and a consequence of this readiness would be the renewal of the Burgundian-Napoli alliance that was signed in 1475, granting the new king Ferdinand II of Naples the knighthood of the Golden Fleece along with a new loan of 300,000 crowns for Naples to use against France.
The battle of Rappollo would signal to Charles VIII that he had to cut his losses while he can. The new League of Venice which consisted of Aragon, Florence, Papal States, Naples, and the Holy Roman Emperor would decisively defeat the French Navy at sea which would scare Charles in terms of being able to supply his lines and began to retreat back into Milan which already betrayed the cause of Charles VIII who now lead by Louis of Orleans who was in charge of the French prescence in Milan would fight a fatal battle for Milan. The threat of excommunication would hang over Charles VIII but fortunately his army was unbeatable in the field with the victory at Seminara, Charles could pursue an orderly withdrawal. This withdrawal would be further solidified by the victory at Fornovo in which Charles decisively crushed the league and continued to march back into Milan with his army and baggage train. The siege of Novara would also further France's position in Milan as Louis of Orleans with now the full French army behind his back drove Ludovico, Duke of Milan out of Milan entirely into the arms of the Holy Roman Emperor. Maximilian at this point still quite strapped with cash from his wars in Hungary and the Fugger Family owning a portion of the income of the twice crowned king would invest Ludovico as Duke of Milan in exchange for a huge amount of cash an a full alliance with Milan.
Burgundy's joining of the war in the last phases of the Italian wars under Charles VIII was merely negotiating forcing the recognition of Ludovico as Duke of Milan and the safe passage back to France. The signing of the peace of Vercelli between Burgundy, Milan and France would conclude the Italian wars de facto and France who at this point under the watchful eye of Peter II of Bourbon would rebuild the navy hastily and continue the withdrawal of French forces in Naples with Gilbert, Count of Montpensier safely returning to France to Charles' delight. The results of the first phase of the Italian wars were clear as Italy essentially was plunder and loot for Charles VIII who used a superior army against various Italian mercenary forces. Burgundy's policy towards Italy was not as shaken compared to the Italian situation as Ludovico now realizing the power of the French, would return to the Burgundian orbit as another ally. The turbulent relation with the Italian states should not be ignored as while the marriage of Margaret of Burgundy to Ferdinand now prince of Calabria was proposed during Charles' Italian wars it would be rejected as Philip rightfully believed an independent Naples would not last, the fact Burgundy did not join the war against France until late 1496 would also push Milan to seek another backer in the form of the Habsburgs under Maximilian which those consequences would be felt in the final Swiss wars. Importantly for Burgundy, France would be forced back but quite pleased with a huge loot chest and a capable army under Charles VIII who would swear to reclaim Champagne and Naples soon after the peace.