Victor Vakatawa, Louis Picamoles and Brice Dulin also crossed, with Camille Lopez kicking 20 points, as France avoided a sixth straight away defeat.
Victory means France keep their slim chances of winning the title alive.
If England do not clinch the title by beating Scotland later on Saturday, any of five teams - England, Scotland, Ireland, Wales and France - could still mathematically win the title in the final round of matches next weekend.
France, who have not finished in the top three since 2011, host Wales in Paris next Saturday.
Italy produced encouraging displays in gallant defeats against England and Wales, holding half-time leads in both matches before fading away in the second half.
Again, the Azzurri ran out of steam.
They have 'lost' the second halves of their four matches this year 115-12, compared to a 57-38 first-half deficit.
Conor O'Shea's side made the perfect start when the talismanic Parisse powered over from close range after three minutes, but they were unable to replicate the defensive resilience shown against the English and Welsh.
The Italians had 53 missed tackles, culminating in a tackle percentage of just 66%, and it was exploited by the French attack.
Les Bleus took the lead midway through the first half when Fickou dummied his way through the Italian defence to score and, although Carlos Canna's penalty reduced the gap to 13-11 shortly after.
Italy crumbled after the break as they headed towards an 11th successive Six Nations defeat, although Angelo Esposito's try in the last play of the game avoided a scoreless second half for the hosts.
However, it was little consolation for a side consigned to the wooden spoon for the third time in four years.
Italy: Padovani; Esposito, Campagnaro, McLean, Venditti; Canna, Gori; Lovotti, Ghiraldini, Cittadini, Fuser, Van Schalkwyk, Steyn, Favaro,, Parisse (capt).
Replacements: D'Apice (for Ghiraldini 63), Panico (for Lovotti 64), Chistolini (for Cittadini 40), Biagi (for Fuser 50), Mbanda (for Favaro 51), Bronzini (for Gori 51), Benvenuti (for Campagnaro 65), Sperandio.
France: Dulin; Nakaitaci, Lamerat, Fickou, Vakatawa; Lopez, Serin; Baille, Guirado (capt), Slimani, Le Devedec, Maestri, Sanconnie, Gourdon, Picamoles.
Replacements: Tolofua (for Guirado 54), Atonio (for Baille 54), Ben Arous (for Slimani 54), Jedrasiak (for Le Devedec 54), Le Roux (for Picamoles 72), Dupont (for Serin 72), Trinh-Duc (for Lamerat 69), Huget (for Vakatawa 63).Referee: Ben O'Keeffe (New Zealand)
Touch judges: Nigel Owens (Wales) and JP Doyle (England)
TMO: Marius Jonker (South Africa). AGENCIES