Far from showing any willingness to go to war with Japan in 1937, France cut off arms shipments to China via the railroad linking French Indochina to China. "The French explained the decision to prohibit arms shipments through Indochina in what came to familiar terms. First, as Premier Camille Chautemps put it, the Japanese, 'in a most polite way but letting him feel the iron,' had indicated that they had long memories and that, should a European war break out, they would remember those who had committed unfriendly acts. Second, the Japanese had threatened not only to destroy that part of the French-owned Haiphong- Yunnanfu Railroad that ran through China but to seize the Chinese island of Hainan, a move that would allow them to dominate the Gulf of Tonkin and which further would place them in a good position to threaten the security of Indochina.23 Simply put, French possessions and interests were too exposed to risk retaliation by Japan."
https://books.google.com/books?id=qovQzYYDv08C&pg=PA111
All this, remember, was at a time when "The attention of most Frenchmen was riveted on the Spanish Civil War, which was at its peak and had produced a severe Mediterranean crisis because of a sharp increase in attacks against neutral shipping in the area. From Paris, the American ambassador, William C. Bullitt, observed, 'The French Government faced by its troubles in Europe is somewhat loathe to take any active part with regard to matters in the Far East.'"
https://books.google.com/books?id=qovQzYYDv08C&pg=PA105
In general, "European considerations dominated French policy toward the Far East. From the very beginning of the Sino-Japanese conflict, the Quai d'Orsay had warned that 'French policy must, in the present circumstances, concentrate its action in Europe.' For this reason, it had been of the utmost importance to avoid involving the League in any far-off enterprise that would only weaken still further its waning influence and thus make it unable to affect the European crisis. As a result of this fear, American support in the Far East had assumed even greater importance. This had been one of the principal motivations for France's support of the idea of a Nine Power Conference, for the conference would directly involve the United States in the issue. But before the Brussels Conference met, of course, the French had made it manifest that the two crises—in Europe and in the Far East—were related. Leger had indicated that 'it was clear that as long as the present tension existed in Europe it would be impossible for France, or for that matter for England, to take part in any common action in the Far East which might involve or imply at some later stages the furnishing of armed forces.' Regrettably, Leger conceded, this situation facilitated aggression in the Far East, but it was a fact and had to be faced.'..."
https://books.google.com/books?id=qovQzYYDv08C&pg=PA166
At least in the absence of US cooperation--which American public opinion made impossible--there is just no way France is going to war for China in 1937. Period.