Why did France give up the war when Paris fell in WW2? Why did they not regroup their remaining army and continue to fight, particularly with British support?
They did not seek capitulation because they lost Paris, they did it because large parts of their amry, and the best part of it, was surounded in Northern France.
The new French government thought that if they offer terms before their army was completly destroyed they could get better terms. They were already thinking about the French position in the Post-War world.