How the French fleet could reshape Britain's 1940 war

If the entire French Navy joined Britain after France fell, would it significantly change the war?

Yes; it would reinforce every major British theater, ease the 1940 destroyer shortage, and complicate Japanese expansion through Indochina.

In this counterfactual, French cooperation would remove the Mers-el-Kébir crisis and add battleships, cruisers, and roughly fifty large and small destroyers when Britain badly needed hulls. Dunkerque, Strasbourg, or a completed Richelieu could change the force available at Denmark Strait. Their availability could also let Hood enter refit earlier. French ships at Alexandria and alongside Force H would reduce British reinforcement demands in the Mediterranean. If the French colonial empire also remained Allied, Japan would have to fight its way into Indochina. That would change the starting positions for operations against Malaya and allow more Allied resources to support Force Z.