Another one of these.
A lot of people seem under the impression Louis cross-dresses. With the exception of his heels, Louis wears men's clothing, albeit a little "sexed" up. Makeup, too, was common during the Baroque era for both men and women, especially among nobility. He doesn't entertain thoughts of dressing like women at all.
... So James wasn't so abject to swapping outfits on account of he's still wearing men's clothing, albeit just a little frillier than he'd like. Louis dressed as James just looks like he took a step back to one of his earliest designs
Louis Despatis and James Hunter © Myself, Shamine A. King