I don't understand how you reached either of your conclusions (viz. that Britain and France needed another country to legitimise the CSA first, and that recognising the CSA would therefore count as an act of neutrality). First of all, if a legitimate treaty with a sovereign nation is all that is needed to make a government legitimate, why didn't Britain and France just be the first ones to sign the treaty, thus legitimising the CSA, thus automatically legitimising their own actions? And if the treaty with Mexico automatically legitimises the CSA, why do France and the UK even need to declare recognition, if it is therefore automatically applied worldwide? If it only takes one nation, then there is no need for any successive recognitions. It's not like there can even be some moral high ground argument here, since it would be pretty freaking obvious from the start that they were just looking for an excuse to legitimise the CSA under your notion.
Secondly, how would this be an act of neutrality? It would be directly weighing into a war by declaring one nation to be in favour while taking a course of action which seriously hinders the other. It's not an act of war, sure, but it's about as much an act of neutrality as the US cutting its imports to Germany to ramp up to focus on British trade in 1915, or signing the Lend Lease agreement to sell Britain 50 destroyers in 1940. About the most unneutral neutral act they could really do, honestly.