Yes, both were looked as pretty hard by Britain And France in the OTL. Britain was as closer than the USA to
annexing Texas as a protectorate in OTL. The Texan Government was under the opinion that Britain was the better choice, right up until they weren't. As Texas Secratry of State, Anson Jones put it bluntly in a letter to the Texan Emissary in Washington DC "Peace with Britain or U.S. annexation and war with Mexico." Britain also had it's eyes on California, I think for lumber production but I'm not sure. Britain's main goal was to curb American expansion, and to find an alternative cotton supplier.
As for France, Mexico owed France so much money that France invaded them twice. It might be possible for France to break off Northern Mexico as payment for their debts. Texas was also on good terms with France, right up until a
herd of Pigs drove the French Emissary out of Austin in 1841. In the 1860's, Napoleon III wanted a buffer state to protect French Mexico from the US. The US had a major problem with the Napoleon III's intervention but was to caught up in the ACW to fight the French.