Except that a Hohenzollern-Sigmaringen prince would be closer related to Napoleon III (his mother was Princess of Baden - daughter of Stephanie de Beauharnais, and while not related, reeked of French empire blood since his grandma was Antoinette Murat). This was, after all, the reason Napoleon proposed Karl of Sigmaringen for Romania's throne. So, maybe with someone who is less likely to see the Bonapartes as usurpers, Napoleon is more supportive of Mexico.
Also, Prince Leopold of Sigmaringen, married Antonia of Portugal (daughter of D. Maria II and her Coburg consort). And it was said Antonia was "dying to be queen, it didn't matter to her too much which crown she picked up". So, that allows Mexico to be better connected with the "liberal" monarchies - Britain, Belgium, Portugal etc.