Dunkirk, the British went home, where did the french go?
Since you asked, approximately 113,000 French troops were evacuated, approximately 40,000 in the rear guard surrendered.
Some French were mixed in with the British and taken to England, others were transported to Channel ports still under French control, where they either surrendered or were caught up in the general armistice. (Some who made it to England were also transported back to France). Only a very small number ended up in the Free French.
In volume II of The Second World War (1949), Winston Churchill wrote of the French defence of Lille that,
...for four critical days contained no less than seven German divisions which otherwise could have joined in the assaults on the Dunkirk perimeter. This was a splendid contribution to the escape of their more fortunate comrades and of the BEF.
The French were poorly lead in WW1 and treasonously lead in WW2. The failure has always been with leadership, not the courage and ability of the French fighting man.