A Head of State does not formally offer an alliance to a foreign non-government group
Where you see the offering of an alliance, I see a cordial, and perfunctory, reply and acknowledgment to a letter written by the former president of France to the current president of the US. Since we are not privy to the all of the day to day correspondence from any sitting president, we can't know how common or uncommon this type of communication is. I'm guessing, more common than we think. As it pertains to this matter in particular however, it's hard for me to believe that any type of hard-and-fast coalition has been made.