Italy
Background to the Invasion
Florence had been at the very center of Italian political life ever since arranging the Peace of Lodi in 1454. This peace was achieved at least in part because Florence had abandoned its long enmity with Milan, hoping that peace would bring financial prosperity, as indeed it had. But there were other players. Venice, had expanded onto the mainland (the terre ferma) and now had a direct interest in the balance of power in the north. Rome, of course, still fretted over control in the center of Italy and feared overbearing neighbors either to the south or the north. And in these years had a couple of popes who thought they could play politics in the big leagues.
Naples was the real flash point, though. In part this was because the kingdom had in the past had Angevin rulers, and the dukes of Anjou were immediately related to the French royal house. This meant that France had claims on Naples. And in part it was simple geography: to get to Naples, a French army would have to pass through northern and central Italy. This, in turn, meant that the northern powers (and the pope) would have to choose sides, should the French ever decide to move.
Milan was another factor. The city was ruled by Ludovico Sforza, who was not a particularly astute ruler. He had a talent for making wrong decisions and for trying things beyond his skill and resources. Any French move into Italy would have to deal with Milan, either as an ally or an enemy.
At first glance it might not seem that Venice would be a direct participant, but Venice had been involved on the mainland for close to a century and now had extensive holdings. Some of those were of great concern both to Milan and to Rome. Any invasion of Italy would necessarily involve Venice.
France
The key player, though, was certainly France itself, ruled by Charles VIII (1483-1498). He was not an attractive figure. Physically deformed, weak-minded and nearly illiterate, Charles nevertheless longed to be a great king. He didn't really know how to do this; he simly longed for the image and reputation. He had been brought up on tales of chivalry and noble deed, including those of his ancestors, and wanted to join their company. He was aware of his shortcomings, of course, and longed for some great deed that would somehow compensate. Italy seemed to provde that opportunity.
Charles had many pretexts for entering Italy. He had a distant claim on the throne of Naples. He could join, or at least claim to join, in a crusade against the Turks. Naples and Milan were in conflict, and Ludovico Sforza had repeatedly asked Charles to intervene. When King Ferrante died, Ludovico had some claim to the spoils of Naples. Many others, in Naples and Rome and France, begged Charles to intervene, and in 1494 he decided to move. While others may have been thinking in terms of power politics, Charles was thinking mainly in terms of knightly deeds and royal fame.