The executive branch can ( via executive order, treasury sanctions, etc ) and of course congress can.
> and how do they enforce payment?
By threat of financial collapse.
> Can the US Government FORCE a French Bank to pay them a fine?
Yes and no. Are we going to invade france and force the bank to pay the fine? No. Could we threaten to place sanctions on the bank and exclude it from international financial system. Yes.
> Surely a French bank could just say "no thanks".
It can. But then it would immediately collapse. No international bank can survive a US sanction because the US runs the international finance system. There is reason why the swiss banking system submitted to US demands to turn over customer data a few years ago. Economic sanctions on switzerland would turn it into north korea or venezuela.
People mistakenly think that US sanctions means that the US won't do business with a certain country. US sanctions means that everyone doing business with the US can't do business with a certain country.
US sanctions essentially forces the world to choose between the US and country X. The US being the largest economy and the heart of the international financial system wins every time.
It's why there is so much drama with US sanctions on iran. It's not that we won't do business with iran. It's that everyone who wants a business relationship with the US can't do business with iran.