In fact, the British offensive was neither hurried nor delayed. After all, the British understood that the main defensive forces of the United States must be in the Northeastern part.
But the French felt more urgency. The land allocated to France was mostly in the Southern United States, coincidentally the target of Mexico's attack.
If the French didn't act faster, they feared that before the French Army could arrive, Mexico would have already taken the capital of Texas, Austin, and Texas would have been smoothly annexed by Mexico.
Indeed, Mexico had a claim of territorial sovereignty over Texas, and the land swallowed by Mexico would definitely not be willingly regurgitated, which would inevitably lead to another war.
But France's current situation clearly did not permit them to start another war. Even a small-scale conflict with Mexico might deepen the French economic crisis.
