If you say so.
31 years here and I have yet to witness or hear anything romantic.
French just sounds normal to me, just as I suppose British accents sound normal to Brits.

From Tom Ellis' perspective:
He tried it with an American accent and said he sounded like a douche.
With a British accent it adds charm to the character.
Say something in a toff British accent it sounds classier. Kinda like saying anything in French makes it sound more romantic.
"Can you keep a secret? Can you know something and never speak of it again?"

From the story's perspective:
Lucifer speaks everything. He said so in the last episode.
He must know every accent too.
He is a guy who loves to score with women, living in the USA, the best choice would be a British accent.
From Tom Ellis' perspective:
He tried it with an American accent and said he sounded like a douche.
With a British accent it adds charm to the character.

Lucifer can speak every language as he elaborated to Dan when he spoke Chinese. One would assume that whichever language he speaks in, he would chose the style that is closest to how the originators speak it. (e.g. when he speaks French he would sound like a Parisian Frenchman rather than a Quebecan, if he spoke Spanish he would sound like a Castilian Spaniard rather than like a Mexican or an Argentinian etc).

I think he may have just chose the British accent as it makes him sound suave haha. Its what he would do. Also Dr Linda doesnt ask him questions because she said in an earlier episode about it being strictly professional But the questions she does ask are really good and lifelike