This could be a grammatically correct sentence if you add a bit of punctuation. While "His enemy is an American" and "The American man is his enemy" are good alternative sentences, you could use the exact same words you originally provided and just add commas:
- The man, an American, is his enemy.
You should also capitalize 'American' here, as I did above. One reason you might want to use the original sentence (with the added commas and capitalization) rather than the alternatives is if you want the subject or topic of the sentence to be "the man."
If it is dialogue, and has a person or character known as "the man" the sentence could also show him saying the sentence "an American is his enemy."
- The man: "An American is his enemy."
You might also say, "His enemy is an American." It is not usual to specify the gender of a person in this context in ordinary conversation. Most Americans would let the other person assume that the American enemy is a male unless the enemy happened to be a female, in which case the speaker might say, "His enemy is an American woman." That would seem to change the whole complexion of the statement. Instead of two males hating each other and fighting, we would imagine a female hating a man and being more secretive and devious about doing him harm. If a man had a serious enemy, the odds would be strongly in favor of that enemy being a man, and therefore the speaker wouldn't consider it necessary to specify that this was the case. In some other languages the enemy's gender would be contained in the noun or pronoun, but this is rare with English. Maybe that is one of the reasons that English is so hard for some foreigners to master.
The sentence "The man an american is his enemy" is not gramatically correct. It should be "The American man is his enemy".