Had France been able to gain some sembelence of control in Mexico by committing enough troops and not trying to run the country thru a proxy Austrian ArchDuke who had began to think more of Mexico's interests than France's then provided that the south could have ethier won the war or at least drawn it out into mid 66 or so. Then yes I believe France would have tried to make a claim on Texas at the very least.
Would it have worked? IMO niether the US or the
CS would have stood for it and there would have been at least a border war with France.