In a dismal match littered with 37 handling errors, the hosts missed two early penalties before two Camille Lopez penalties and one from Scott Spedding gave France a 9-0 halftime lead.
The second half was a slight improvement as Yoann Maestri and Mathieu Bastareaud scored the game's only tries while Jules Plisson kicked two penalties and two conversions after replacing Lopez, who suffered a knee injury.
"In the first half we were able to wear them out physically and we were at their throats in defence," French coach Philippe Saint-Andre told reporters.
"It wasn't a perfect match but we'll take all the positives from it and today we had a real French team."
France, who visit England for their final game next Saturday, have four points while Italy, who host Wales the same day, have two. England, Ireland and Wales all have six points.
Sergio Parisse made a record 112th appearance for Italy, surpassing Marco Bortolami's record, but it was not an afternoon he will want to remember.
A chilly, rainswept day and a wet ball meant neither side was able to produce much flowing rugby but Italy coach Jacques Brunel was not looking for excuses after his side failed to find a way through in attack.
"The rain wasn't our problem, the French defence was, especially in terms of winning the ball and shaping our game. That's where we had problems, not with the weather," he said.
Italy's problems began when Tomasso Allan, brought in at flyhalf after Kelly Haimona pulled out of the match through injury, tweaked his groin in the warm-up and began the game with strapping.
Allan was quickly in trouble, wincing after sending the first penalty of the match high and wide, and went off after 14 minutes, to be replaced by Luciano Orquera who almost immediately struck Italy's second penalty against the post.
Spedding missed France's first penalty kick from a difficult position but the first points went on the board in the 29th minute when Lopez kicked a penalty from halfway inside the Italian half.
Both teams wasted chances but, in between the mistakes, Lopez kicked France further ahead and Spedding added another with the last kick off the half.
Plisson extended the French lead at the start of the second half after Parisse was penalised for not releasing.
France then produced the first decent move of the match, sparked by Spedding's run and ending with a try by Maestri which was converted by Plisson.
Plisson kicked France further ahead as they took control and Bastareaud's try, again converted by Plisson, completed the French win.
(Writing by Brian Homewood in Berne; editing by Toby Davis)
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