Picard appears to speak fluent French. Not only was he born and raised in France but we see him speaking French confidently with a French accent, swearing in French under his breath and singing French songs on multiple occasions.
The longest instance of Picard speaking (what appears to be fluent) French is from TNG: 11001001
MINUET: Aren’t you going to introduce me?
RIKER: Captain Picard, this is Minuet. Minuet, Captain Jean-Luc Picard.
MINUET: Enchantée. Comme c’est merveilleux de vous voir ici.
PICARD: Incroyable ! Vous êtes Parisienne ?
MINUET: Au fond, c’est vrai, nous sommes tous Parisiens.
PICARD: Oui, au fond, nous sommes tous Parisiens. The spirit of that city can always enchant my soul.
Notably, he recognises her accent as being "Parisian" rather than just "French" which suggests a reasonable degree of experience of French regional accents, presumably as a result of his having been born and raised in Labarre, France.
He uses a little bit of French in TNG: Elementary, Dear Data
(and again in TNG: The Last Outpost).
In TNG: Chain of Command, Part II he states that his family would sing songs in French each week.
PICARD: Sur le pont d’Avignon, on y danse, on y danse.
MADRED: Wake up. Where were you?
PICARD: At home. Sunday dinner. We would all sing afterward.
He sings Frère Jacques in TNG: Disaster
PICARD: I’m afraid I don’t know that one. I know. Frère Jacques. That’s a song I used to sing when I was at school. Patterson, do you know that one? Good. It goes like this. “Frère Jacques, Frère Jacques, dormez-vous? Dormez-vous?”
ALL: Sonnez les matines, sonnez les matines, ding ding dong, ding ding
PICARD: Very good. Now, keep singing.
ALL: Frère Jacques, frère Jacques, dormez-vous? Dormez-vous? Sonnez
les matines, sonnez les matines. Ding ding dong, ding ding dong. Frère
Jacques, frère Jacques, dormez-vous? Dormez-vous? Sonnez les matines,
sonnez les matines. Ding ding dong, ding ding dong. Frère Jacques,
He sings Auprès de ma blonde with his brother in TNG: Family
PICARD(S): Auprès de ma blonde, qu’il fait bon, fait bon, fait bon…
Dum, dum, dum…
Moving down the canon scale, in the EU novel A Time to be Born, Picard’s mother carries on a conversation in French with a teenaged Jean-Luc at home. It’s not clear what language he’s speaking since the conversation is translated for the reader, but he definitely understands her.
“Here, Jean-Luc, eat your lunch,” said a feminine voice speaking
He whirled around to see his mother carrying a tray of food
into the room; she set it on his desk and smiled at him. He glared at
the wall where the picture window had been in the cabin, because he
assumed they were watching him. “I know that’s not my mother.”
The novel What Lay Beyond confidently states that French is his mother tongue:
“May I help you, Captain Picard?”
Startled, the captain looked at the interface and saw its expression
had not changed. The words were in French, his native tongue.
“Yes, you may,” he said in the same language. “How do I disengage the
The novelisation for Generations states that his conversation with his wife and children in the Nexus is in French (with the proviso that this is a weird alternate dimension where weird things happen).
“Go on....” A soft voice at his elbow took him aback. He whirled, and
saw his gentle captor—golden-haired, straight, slender—smiling at
him with the same indulgent love in her green eyes.
He had never met
her; yet he knew that this beautiful creature was Elise, his wife of
the past sixteen years. And she had spoken to him in French.