I don't know if there was any particular political debate on the matter, but there would have been a significant military problem.

More important than Italy, the Germans tended to attract French attention, and the remilitarisation of the Rhineland provided, if anything, the best cassus belli that the French had in the interwar period. (Excepting colonial details like the Rif war). But the French military could do nothing.

The problem was the way they were structured. The French military was designed to win the next Great War, a huge, multi-year battle between fully mobilised nations at arms. Total War. Kindof what WW2 turned out to be, actually. However, because everything was designed around expansion of personnel and industry, it also meant that there was very little available for what we would today call contingency operations. The question of conducting a military operation against Germany in response to the Rhineland move was, indeed, brought up. The government was basically given a binary choice: We can do nothing, or we can mobilise the entire country for a full-on war. There was no in-between option.Of course, as we know, the French government decided to go with Choice A. There is no reason that Italy would have provided a better choice as the same Army would have been used for that as well.