How would they? The French were invading them during the ACW and the republicans and imperials were fighting until 1867.
Aside from that, the Union supported the Mexican republicans. Unless Maximilian somehow wins within 3 years, has the country recover enough to launch an invasive rather than fight a protracted civil war of his own against the republicans, and has French support against the CSA and the inevitable Union counterinvasion, it's not feasible to see them move any troops.