@delaja If you look at the National Reference Sheet for Free France, at the time Free France is formed, Free France chooses a capital.
Then, when Paris is liberated, this rule applies: Page 45, Capturing an Enemy Capital, “If a nation relocates its capital, it can be moved back at any time if again in Possession.”
I think the word, “can” would indicate voluntariness on the relocation of the Free French capital back to Paris. I’m not positive about this, but I’d argue that Free France doesn’t have to move their capital back to Paris again, so they would not lose their income or have to relocate their capital again.
One other interesting question is if Free France becomes a major power (when Paris is liberated), if the Axis recapture Paris, does Free France lose its major power status, or, like China CCP/KMT, once it becomes a major power again, does it remain a major power?