The Mona Lisa was actually in France quite close to DaVinci's death; he seems to have brought it with him to France when he moved there late in his life at the invitation of Francis I. This is not terribly surprising; other Italian artists like Cellini were invited to work at Francis's court as well. Francis later brought the painting very soon after Leonardo's death, probably via his assistant Salai who inherited the painting and it has been in the French royal collections(first at Fountainbleau, where several early accounts describe seeing it and a number of copies were made at various point, and then Versailles until the French Revolution and the transfer of the royal collections to the Louvre) and then the Louvre ever since.