French filed docs, obtained by TMZ, seeking to trademark his name for commerce in the health and beauty market. French says he wants to put his name on fragrances, non-medicated lotions and shampoos, and non-medicated toiletries.

As French might say ... smellez-moi!

Now, he's also applied to trademark his name on almost anything you can buy: jewelry, tote bags, backpacks, beach towels, watches, kitchen linens, sunglasses, pillow covers, headphones, and all kinds of clothing ... including underwear.

Seems like he's mostly trying to block anyone else from making dough off his name, but the perfume could work -- Remind her she is ... Unforgettable with a scent by French!