Staying within otl fund limits for all but Maginot--
which is what I'm working with here--there might be one other option the French could have:
if we assume the heer comes into Belgium as otl, the French might send a more limited component into Belgium.
Suppose they sent in only forces equipped with AA--but more of those--ittl?
This wouldn't require additional funds or personnel, just a tactical shift of some of those.
Then, the only sizable ground forces facing Hitler in Belgium would be the BEF and the Belgian army, with just this small AA French component.
The Luftwaffe might still take heavier casualties than they'd anticipated, since they MIGHT have assumed France would not enter Belgium, being as how they've extended the Maginot Line to include the whole length of the Franco-Belgian border.
Thus, the move of French AA would have a last-minute, surprise quality to it, that might still produce higher Luftwaffe casualties in Belgium than otl.
We might also, that way, still have the option of a Belgian and even Belgian/British, withdrawal, into the Maginot Line--instead of, say, Dunkirk.
Then, the later British withdrawal would come straight out of France.
But, we're still facing a huge airborne Wehrmacht component we didn't face otl at this point in the War.
Now...If it gets cut up enough by the BEF and some kinds of French maneuvers--such as the hits on armor via the Maginot-housed Char B "Shadow" heavy tanks that were equipped with the 75 mm guns--we might get some additional hits on the Wehrmacht, just as we've already shaken up the Stukas. We could extend Maginot's effective range quite a bit that way.
If the French could then, say, dig in and begin some new trench warfare scenario--for which they were still excellently equipped and for which the Germans have little more patience than they do--they may be able to develop a new psych warfare option against the frenzied heer, which wants to get this over with so it can focus more East.
Against these paratroopers, a lot might hinge on how effectively the French air arm and the RAF can take down Luftwaffe transport planes, parachutists and gliders. If they can do enough damage at that point to the ability of the heer to land Panzers, etc., to back up the admittedly more numerous Wehrmacht air airborne infantry, and can do a little more, as well, via the attacks outward from the line by the Char B heavy tanks, at least at a few points (the French only had about a dozen of those, and I have no money to add any more to the French arsenal), we could produce a somewhat more successful campaign in France.
It's even possible that the "real" aerial Battle of Britain might be fought over France, with that wrinkle.
However, insofar as a successful air cover against the Luftwaffe, the French are still, on balance, unlikely to retain their air bases. Germany has more materiel it can get into France by air. We may come darned close, however, to keeping the Char B heavy tanks operational for the duration of the Battle of France. It's just that, to avoid air attacks, they'll have to range only a certain distance from the Line.
Once the Wehrmacht has captured or destroyed the French airfields, the only effective air in France will be via the RAF. However, it's slightly possible the French air force might consider using British airfields to extend their active life somewhat.
As for the Italians, assuming they still come in as otl, they'll be more inclined to be using airborne forces, as well, though perhaps, as noted earlier, not as extensively as the heer because they don't have the additional financial resources.
We've got, I hope, the Free France fleet in more sizable numbers this time around, so that can help cope better with Mussolini.
Anyway, the Brits are also somewhat still geared to WWI here, too. So, with a bogged down quality setting in for the (hopefully) less well-armored Wehrmacht, Hitler may decide to get antsy and go for terror air attacks on French civilian targets.
It might depend on how that fell, where that fell, and how it is registering with the "wavering" among the French, when coupled with the "defeatists" or "fatalists" among the French, as to where that puts us on the scale of a more successful armistice negotiation.
If I'm putting things together right at this point, there's a real potential that we have less readily-available Luftwaffe on hand in western Germany, Belgium (if Hitler is there) and over France, than otl. To get much more Luftwaffe resources, he's got to pull some west from east--at least, for a shot shot military usage of the Luftwaffe.
If he decides to commit the Luftwaffe to hitting largely civilian targets, I can see how that would have a real potential to weaken French will here.
It's then going to be a psychological thing: who would crack first, in a bogged down trench warfare scenario with limited armor, after all?
Well, I can't say the French can actually win, militarily, here, but the key is to get on Hitler's nerves enough about the clock for Barbarossa and the repositioning of forces from it, to be able to get a more favorable Armistice.