Philippe Saint-Andre's men had shown plenty of cause for optimism with a strong performance in a narrow 26-19 defeat to New Zealand last weekend.
And they continued to show signs of improvement at the Stade Oceane in Le Havre, with the hosts scoring four tries in a game that saw both teams reduced to 14 men.
Scrum-half Morgan Parra gave France the advantage with a penalty inside the first two minutes, before Sofiane Guitoune increased the lead to eight points shortly after with a try on his debut.
Fly-half Remi Tales was the creator, with his perfectly-placed kick gratefully collected by winger Guitoune to touch down in the corner.
The boot of Parra continued to be France's main source of points, though, as the Clermont Auvergne man added two further penalties to take the lead to 14 points two minutes before the half-hour mark.
Tonga fly-half Fangatapu 'Apikotoa did get the visitors on the board with two three-pointers of his own, but their hopes were dealt a blow when scrum-half Taniela Moa was sin-binned in added time in the first half after a reckless elbow.
France quickly took advantage as number eight Damien Chouly scored their second try to move Saint-Andre's men 21-6 ahead at the break.
Tempers frayed directly after the interval, with France's Yoann Maestri and Tonga's Sona Taumalolo dismissed following an off-the-ball scuffle.
Talented fullback Brice Dulin exploited the extra space to cross for France's third score 10 minutes into the second half, although winger Fetu'u Vainikolo responded for Tonga six minutes later.
A dramatic fightback never materialised, though, with a fourth penalty from Parra and a Benjamin Kayser try wrapping things up for France, despite Vainikolo's second in the final minute.