The POD is either in 1848 or 1853 regarding a war that started in 1861. I'm not really sure there'd be many butterflies preventing the French invasion of Mexico.
The french invasion of Mexico was a response to a specific situation in which the Mexican government failed to repay loans to French creditors. If you disappear two massive populated states, you massively change the Mexican political situation. Some of the debts may never have been accrued, the French may have been paid back, or whatever. A President Juarez is very unlikely in this scenario, given how random his ascension was OTL. The Mexican civil war might not have happened, but if it did, it would certainly have happened differently. Mexico might have easily collapsed into more than one state, the Mexican government without Sonora and Chihuahua is much weaker. Conversely, as I've said in other places, a TL where the US occupies large areas of actual populated Mexican territory rather than Indian wilderness results in resistance. A rebellion could be supported by Mexico and an intelligent response by the British (diplomatically) and French (militarily) would be to support them.
This whole thread is a bit like a confederate victory timeline asking whether Greeley would have beaten Grant, you are all thinking way too small.