Scrum-half Yachvili added two conversions and two penalties to ensure France hit the ground running as they seek to put their World Cup final disappointment behind them.
That 8-7 defeat to New Zealand in Auckland saw Marc Lievremont's reign as national coach come to an end, but Yachvili is excited about how his replacement has taken to the job.
"We started to learn his new mood, his new vision for the team," said Yachvili, after France had just six days preparation with Saint-Andre.
"We're still learning, but it's cool. France are happy to start this competition with a win.
"I think Ireland, England, Wales, Scotland are also favourites. Many teams can win the Six Nations this year.
"For sure we were second in the World Cup so everybody's waiting for us so it's going to be very hard."
Clermont's Rougerie and Malzieu helped France into a 15-6 half-time lead, before Clerc and Fofana went over after the break to cap off a convincing display.
Italy were also adapting to a new coach, but Jacques Brunel was unable to spring a surprise despite a spirited first-half performance.
Tobias Botes kicked a penalty for Italy while Kris Burton landed two others and a drop-goal, but it was not enough.
France host Ireland on February 11 in their next match, while Italy will seek improvements at the Stadio Olimpico against England on the same day.