this is quite interesting. OED2 has two separate entries for these:
employé - One who is employed. (In Fr. use chiefly applied to clerks; in Eng. use gen. to the persons employed for wages or salary by a house of business, or by government.) Hence also employée, a female employé.

employee - orig. U.S.
[f. employ + -ee.]
a. A person employed for wages; = employé, which it has now virtually superseded. b. (nonce-use.) Something that is employed.


so, if this is to be credited, we have two separate words with unique derivations -- the U.S. entry formed in the usual manner of adding -ee.

some years ago I remember seeing the 'employe' spelling (with no accent) in our company newsletter. they used it consistently for some time, but then it fell out of vogue again.