Sounds like you're actually inquiring about IMPORTING the vessel, not just registering it.
Both posters above are correct. If you're going to be cruising internationally, you'll want to have the vessel federally documented. Otherwise, state registration is sufficient. But these are entirely separate considerations from importing the catamaran.
It's very simple to do. I recommend researching it online, then contacting the Customs and Border Protection offices at several US ports of entry. The reason I say several is that when we imported our boat, we received very different information from the three different offices we spoke to. One was primarily familiar with land vehicles, one was primarily familiar with ships and large commercial fishermen, and the third was the one...familiar with recreational vessels...that had the information we needed. We did the paperwork ourselves and it was very straightforward and cost us nothing because of NAFTA. Your catamaran, having been made in France, would naturally be subject to duty, but the actual process is quite simple.
The process of importation into the US didn't require a HIN, which our vessel didn't have. When we registered with the state we were assigned one, had two small engraved plaques made, and epoxied them in place.