|Let me play devil's advocate:
What if the other allied countries supplied troops in the same proportion as France did for the Battle of France?
France had mobilized 6m troops (!) and had stationed 2.2m in the North of France. All the other allies combined only contributed 1.3m troops (UK, Holland, Belgium).
While France marshalled 93 divisions, UK only marshalled 10, Holland 9 and Belgium 22.
The French military actually surpassed the Wehrmacht in numbers.
The question is, what would have happpened if the Allies had mobilized troops in proportionate numbers to their populations?
This would have brought allied numbers up by millions. This means that France would have had strategic reserves (which they didn't in the actual battle) to defend Paris, to threaten the German A Group (the 'Sichelschnitt').
It would have greatly increased the morale of the French political leaders and although losses would have still been heavy in the beginning, like the Russian campaign, despite the huge initial losses, the Allies would have the strategic reserves and strategic depth (in Bretagne and Normandie) to launch counter attacks.
Paris would have become the French Stalingrad, as the German army met the million man + Allied reserves in street to street battle. Despite their early gains over the Allies on the relatively flat plains of Picardie and Champagne, in the urban environment, faced with millions of French, Brits, Poles, Czechs, Dutch and Belgians, the Wehrmacht's vaunted tactical mobile prowess would have come to nought and superior Allied numbers would, after a long bloody contest, have won the day...