Little seems to be referenced in the books I've read about this area of the war. I would suspect the mountainous terrain was deemed unfavorable to large scale combat. The maps I've seen show a scarce few assorted French units and seem to leave out any Axis units that would have been in the area entirely. Was it primarily defensive operations on the Allied side or were there ever plans for larger scale actions against Northern Italy from France?
I don't think the Allies ever seriously considered an assault on the French Alps.
During Dragoon, Patch had information from Ultra intercepts that there were no major Axis units in the area. But once he began to advance up the Rhone valley, he kept his Airborne and some other minor units guarding the area, to prevent anyone from hitting his flanks. Eventually these were replaced by the French units you mention.
Once Dragoon was complete the goal was always to cross the Rhine and get into Germany proper as quickly as possible. The Italian forts led nowhere useful, contained no real force to be concerned about, and would cost a disproportionate number of men to take. Already the Italian campaign was seen by a lot of leading allied commanders as a sideshow to the real war. And from central Italy there was a real chance to punch through to the Po Valley. The French Alps offered a significantly harder slog to the same area. So it was seen as even less enticing.
I'm not aware that even Churchill ever suggested an attack on the French Alps. And he was generally the most enthusiastic Allied leader for alternative paths to Berlin.