"The agreement will commence at the beginning of the 2018 championship and TF1 will show four Formula One Grand Prix races in exclusivity on free-to-air in their entirety," Formula One said in a statement.
The other races will be shown as highlights.
Vivendi Group's Canal+ pay television channels currently have the right to broadcast all grands prix in France and agreed a new multi-year deal in May with the sport's new owners Liberty Media.
The French Grand Prix is returning after a 10-year absence next season with a race at the Le Castellet circuit near Marseille.
France has two current drivers in Haas's Romain Grosjean and rising star Esteban Ocon at Force India while manufacturer Renault has its own factory team and supplies engines to two others.
Ferrari-backed Monegasque racer Charles Leclerc is also leading the Formula Two feeder series and is expected to enter Formula One with Sauber.
Ian Holmes, Formula One's director of media rights, said the TF1 deal would "significantly help to further elevate the sport in the market."
Formula One has faced declining television viewing figures in recent years, with the sport increasingly on pay television, and Liberty are keen to build the audience since taking over in January.
"Free to air is critically important to us," the sport's commercial managing director Sean Bratches told an FIA conference in June.
"My vision as it relates to media rights is a hybrid of free-to-air and pay. Our plan is to balance the two but have a prominent, over the year, free-to-air voice. That is important from a fans, sponsors and relevance standpoint."
(Reporting by Alan Baldwin, editing by Toby Davis)
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