France lead the standings with 15 points from second-placed Scotland on 11, and are in a strong position to retain the title. Italy remained in fifth place on five points.
France burst into a 19-0 lead at the Stade Pierre-Mauroy with tries from Louis Bielle-Biarrey, Emmanuel Meafou and Tomas Ramos to put them comfortably ahead before Ange Capuozzo dotted down for Italy to make it 19-8 at half-time.
Debutant winger Gael Drean and centre Emilien Gailleton added two more French tries in the second half.
Ramos converted four of the five tries while Paolo Garbisi put over a penalty for the visitors.
France took the lead early as captain Antoine Dupont’s kick in behind the Italian defence allowed Bielle-Biarrey to chase and score for a record-breaking eighth Six Nations game in a row.
French full-back Theo Attissogbe and Italian winger Louis Lynagh duelled on the halfway line under an Italian high kick, with Lynagh knocking it back where Dupont collected the ball before kicking it on.
The second try came in the 15th minute as France drove at the Italian line with Ramos, and then Drean stopped metres from the try line, before Meafou used his power to go over and score his first test try.
The lead was stretched in the 29th minute as a poor throw from Giacomo Nicotera in front of the French 22-metre line allowed Gailleton to pounce on the loose ball and try to break before passing inside to Ramos, who dived over in the corner.
Italy reduced the gap before the break as Ramos and then Attissogbe were snagged in front of their own try line with the ball spilling for Capuozzo to react quickest and touch down with a cheeky touch.
It took until eight minutes from the end for France to get a fourth try with Ramos kicking out to his right wing, where Drean went over in the right corner.
The fifth and final try came three minutes from time when Attissogbe broke through on the right wing before feeding Gailleton, who broke Paolo Odogwu's tackle to score.
"It's a five-point victory. In a competition where there's a title at stake, that's what matters most. It wasn't our most polished performance, that's for sure, but I can tell you that the Italian team made us work for it," said Ramos.
"It was a tough match, as expected, very tight, with an opponent who put us under pressure in possession, especially in the rucks, and who were good in the air," added coach Fabien Galthie.
"At one point, we got into a real battle. We tensed up, but we managed to find that extra bit of energy to turn the tide and secure the attacking bonus point at the end of the match," he said.