Part of the reason France left Mexico, other than having major supply problems and a new understanding that the Juaristas were not pushovers, was that in the early Spring of 65 the US consul expressed serious displeasure w/ having French troops on the border.
I'm paraphrasing the conversation. And can't recall the source.
"You need to move your troops away from our border."
"Meaning what?" The French Consul asked.
"75,000 US troops in Mexico city in 10 weeks."
Stunned silence. "Understood."
What certainly struck home was not the threat of a US intervention in Mexico but the candid, and reasonable, estimation of how long it would take to get US troops into the heart of Mexico. At that time the US had a very respectable standing army in the field w/ a doomed CS before it and that army was no longer green.