If Austria is unable to fight France over Milan then Francis will feel free to try to take back Naples and without Spanish support Austria will be unable to fight France over Milan as they have already to keep France out of Burgundy.
It was not that simple and the term "Austria" is anachronistic in this context so I assume that you are talking about the territories hold in that AH by the Hapsburgs. As an Emperor, Charles V had access to the German military resources (landsknechts), which provided him with a much more modern army that the French had. Plus, it could be almost taken for granted that as soon as one side is winning, there is Italian coalition trying to prevent it for getting too strong. With his finances being generally in a better shape than those of "Charles minus Spain" Francis or his successor could win in a long run but the war would be too exhaustive for starting a brand new one over Naples with an opponent who was growing his strength (both military and financial) by staying in a relative peace.
As for the Burgundian Inheritance, it is mostly more of the same: an exhaustive war which
may end up in a French favor because the Hapsburgs are going to run out of money first but in which France is still handicapped by the fact that, in general, the Hapsburgs have access to the better infantry. BTW, IIRC, fight in the Lorraine & the Low Countries started seriously after Milan was lost so it is not necessarily simultaneous war on two fronts.
Anyway, the main problem of the early XVI warfare was that it was rather difficult to achieve a "Napoleonic" victory allowing to end a war by a single battle (unless you get lucky by capturing enemy's King but even then almost as soon as he is out, the war can restart). A great victory was routinely ending up with the sieges and occupation of the fortified castles and town and the big armies had been disappearing due to the diseases, needs to garrison the taken places and absence of the funds. So the critical question (to which I assume to referenced) is for how long in this AH the alt-Charles V (or whoever) is capable to finance a major war? IMO, for a much shorter period than in OTL but long enough to prevent Francis & Henry II from the further adventures.
Actually, if we are completely free in our speculations all the way to assuming that between Louis XI and Henry IV France has couple kings with the brains, the whole strategy of the Hapsburg wars could be different with a stress upon the Northern/North-Eastern border of France (Lorraine, Alsace, French-Comte, Low Countries). This was pretty much happening under Louis XIII and Louis XIV (prior to the WoSS) and it did make a practical sense while Italy not too much. Of course, Milan of the early XVI was seductive by its wealth (which Lodovico Moro paraded for everybody to see) but Naples was not even too rich and none of them could be realistically integrated into France (but the people of that period did not see things that way and personal union was OK).