Although it seems that the British agreed to let France acquire six state-level administrative regions, including Louisiana, Mississippi, Arkansas, Oklahoma, Texas, and New Mexico, the British actually had profound intentions.
First of all, these six states definitely do not compare to several of those on the United States East Coast, and the British will assuredly gain far more than France will.
Secondly, Texas and New Mexico were once part of Mexico, and the United States had fought multiple wars with Mexico over these areas.
After France takes over these areas, whether Mexicans in these two states will seek independence is an issue, as is Mexico's attitude.
Although the French are far stronger than the Mexicans, the dissatisfaction of the Mexicans is destined to make French rule in these states much more difficult.
Being able to disrupt French rule, while apparently gaining a lot of territory for France, is a situation where the British naturally won't say much.