We played it last night along with the Susato Pavanne, Mille Regrets and the Josquin Mille Regrets. It's the imagined reply to the speaker in the original chanson. Like Christopher Marlowe writing Come live with me and be my love and Walter Raleigh writing If all the world and love were young, and truth in every shepherd's tongue.
I transcribed this from London Pro Musica EML 234. Usually LPM are good about providing translations, but if this edition has one, it's been lost from my copy.
I think the gist is that the speaker in Mille Regrets is really sad to be going away, and the responder in Les miens aussi is sad, too, but probably only for a brief time.
But if you know more 16th century French than I do and want to provide a translation, it will be welcome.