The direct translation would be something like "she loves you in the American way not the French way".
1.) Is this an idiom?
2.) If it's not an idiom, what is meant by "l'americaine" and "la francois" in this context?
The full letter can be read here
The relevant passage is this one:
In spite of Schuylers black eyes, I have still a part for the public and another for you; so your impatience to have me married is misplaced; a strange cure by the way, as if after matrimony I was to be less devoted than I am now. Let me tell you, that I intend to restore the empire of Hymen and that Cupid is to be his prime Minister. I wish you were at liberty to transgress the bounds of Pensylvania. I would invite you after the fall to Albany to be witness to the final consummation. My Mistress is a good girl, and already loves you because I have told her you are a clever fellow and my friend; but mind, she loves you a l’americaine not a la françoise.
Adieu, be happy, and let friendship between us be more than a name
A Hamilton
The final consummation referenced here is Hamilton's upcoming marriage to Elizabeth Schuyer. The reference to the "bounds of Pennsylvania" is about John Laurens' parole terms which kept him restricted to Pennsylvania.
I would translate it "as an American (woman), and not like a Frenchwoman".
The free morality of the french is being used as a foil for him to basically say "my wife likes you, but not in a sleep-with-you kind of way"
At least this is my best interpretation, if it's an idiom it's new to me.
EDIT:
It was new to me. JanitorJasper has convinced me that "in the American way" is superior to my translation. I still think that the sense in English is the same as before, i.e., "don't get too excited"
be witness to the final consummation
These days, "consummation" is something most people wouldn't want their friends,family and clergy to witness. Did the meaning change over time from "getting married" to "getting some, for the first time after getting married"?
I just stumbled upon this thread through a Google search. I have a copy of Grotius signed by Alexander Hamilton. On the cover page, I believe John Laurens' name is on the left (word in the middle) and Alexander Hamilton's name on the right.
See attached imgur album.
Image 1 - Signature
Image 2 - Cover