Why avoiding the Great Depression might not rescue France

Would France fare better in World War II if the Great Depression had not occurred?

Probably little better, because political distrust of France's own armed forces would remain the overriding problem.

Removing the Great Depression does not automatically repair France's prewar position. In this answer, political distrust of the armed forces remains the overriding problem. That distrust would still affect how the state prepared for war even if the economic shock were absent. The counterfactual changes one condition while leaving the central political constraint in place.