How a continuing French fleet reshapes the Bismarck hunt

Why send Hood against Bismarck if Richelieu is available in a French-fights-on scenario?

Because the Allies could field several separated task groups, while French support elsewhere changes refit and readiness across the fleet.

Richelieu and other French forces could create additional Atlantic groups rather than simply replace Hood in one encounter. French ships taking part of Force H's burden would release British units for other task groups. Reduced Mediterranean wear on Ark Royal and other ships could alter their availability months later. Hood might even enter refit earlier, showing that the counterfactual changes maintenance and readiness as much as the visible order of battle.