Not a bad idea. Inasmuch as his widowed mother the Empress Eugenie and Queen Victoria had befriended each other during the Great Exhibition of 1850 and would stay good friends with each other to the end, I could imagine the Prince Imperial possibly considering wanting to marry one of Victoria's daughters- either the older but fetching Louise or the plainer but younger Beatrice. However; as much as Victoria sympathized with the Prince Imperial and Empress, what would it have gained Victoria to have had one of her daughters marry the son of a deposed monarch -especially since France became a staunch Republic after the Franco-Prussian War was over and done?
Also, the Spanish-born Empress Eugenie herself had been a VERY devout Catholic and had kept that faith quite close to her as a means to cope with the late Emperor's flagrant infidelities. Hence, the Prince Imperial more or less would have had to considered it a virtual certainty that he'd have been disowned by his surviving parent had he openly expressed a wish to renounce Catholicism and even had he had a separate income, would he have been willing to risk that?
The terrible irony is becoming a soldier-of-fortune for the nation that had given him and his mother a comfortable refuge may have been one of the few fates the Prince Imperial could see for himself besides puttering around and hoping to eventually see if the parents of a Catholic princess would be interested in arranging a marriage to the exiled heir of a lost Empire.