Canada and Poland were actually vital to the liberation of France. They landed on the beaches, and helped close the Falaise Gap, in which otherwise the Germans could escape and kill may more Allied Forces. The Polish also had an armored division, in which I haven't heard the Free French had one.
Then I give you the "2e Division Blindée" (that's an armoured division to the anglophones), formed on 24 August 1943 in Témara, Morocco, commanded by General Leclerc!
It was refitted with US Shermans in late 1943 and then debarked in Normandy. It was the division de Gaulle badgered the Allied command to dispatch to capture Paris, once the Parisians had started their uprising against the German occupiers.
Otherwise the "2e DB" was one of the crack divisions Patton had at his disposal for beating up German armour, which they did with a certain gusto. Patton was full of praise for the unit. He recognised a good thing when he saw it.
Apparently they were part of General de Lattre de Tassigny's 1st French Army to pitch into the German forces holding Alsace and Lorraine. The 2e DB captured Strassbourg on 23 November 1944.
Since de Gaulle demanded it as a political necessity for the reconstituted French army to take indepedant action, the 1st French Army then crossed the Rhine into German proper. It was the "2e DB" who arrived first at Hitler's villa at Berchtesgaden as well, a couple of hours before the US 101 Airborne.
The division lost 1 687 men KIA, 3 300 WIA. It lost 58 for 118 German tanks destroyed (including taking out a Tiger positioned at the Place de la Concorde itself, managing not to blow up the obelisque of Ramses II right beside it, for no own losses). It killed 4500 Axis soldiers and captured another 8800. It had a 2:1 kill rate of German late-war Panzers, using Shermans. Not too bad.
The unit is kind of ridiculously famous in France, if enough Anglophones were only paying attention.
As for the French not landing on the beaches of Normandy on D-day, that's because Roosevelt didn't really want to have French troops liberating France at the time. There were 400.000 French troops in allied service by then, so nothing was really preventing the planners from giving them a beach of their own to storm, had they wanted to.
Otoh a little while later an entire French army hit the beaches of the Mediterranean and overran the German garrisons fortified in Toulon and Marseilles at absolutely break-neck speed.
So the French army was actually fighting like devils more or less independantly in the south and east of France, not under the immediate supervision of Canadians, Poles, British, Americans etc. in the west and north.
