More likely, she would be the French equivalent of a "Jane Doe" or someone else who they could not prove their identity.

The more questionable/compelling scenario would be if she had some sort of contract in her name - loan, credit card, lease, whatever - and whether it could be enforced. At that point, the plaintiff would have to prove that a) the contract was valid and b) it was with her.

Of course, since she doesn't have any form of ID, whatever notarization-equivalent wouldn't be possible.

Or maybe, that's the loophole? Sign a contract with her for some small sum. She breaches the contract. Now sue her to prove her status and identity?

My God, what a mess.

I'm pretty sure they can prosecute John/Jane Does, so I don't think they'll have any problem saying she's not who she says she is, because that person is dead, but she is someone, even if they don't know who.

Or... because you no longer exist as a legal entity, everyone has free reign to hurt you in any way they please without legal repercussions

This is actually the original definition of an outlaw. You were outside of the law, and no longer under its protections.

They do mention police threathened to arrest her for "driving while dead". I don't put it beyond bureaucracy to imprison a "corpse" just because it's more convenient

I did imagine something along those lines while reading, though. She'd made a badass invincible assassin for hire