Jonathan Rea finished third in the first World Superbike race of the weekend at Magny-Cours as Toprak Razgatlioglu won on his Pata Yamaha.
Series leader Alvaro Bautista suffered a mechanical problem in the early stages but recovered to work his way through the field to take 10th place.
Razgatlioglu's win, his seventh at the French circuit, reduced his arrears to Bautista to 55 points in the standings.
The Spaniard had led by 74 points before Saturday's race.
Kawasaki rider Rea extended his run of podium positions after finishing on the rostrum three times in the previous round in the Czech Republic six weeks ago, including his first win of the season.
The six-time champion from Northern Ireland announced earlier this week that he would be switching to Yamaha power for his 2024 campaign.
Ducati-mounted Bautista hit the front on the opening lap, but title rival Razgatlioglu overtook him, before the defending champion suffered his technical problem on lap three of 20.
Razgatlioglu then became involved in a thrilling battle with Michael Ruben Rinaldi at the front, the Turkish rider eventually getting the better of the Italian.
Pole position man Garrett Gerloff, Danilo Petrucci and Andrea Locatelli completed the top six positions.
The Superpole sprint race and Race Two will be staged on Sunday, with another three rounds of the series to follow thereafter.
World Superbike standings
1 Alvaro Bautista (Spa, Ducati) 433 points
2 Toprak Razgatlioglu (Tur, Yamaha) 378
3 Jonathan Rea (GBR, Kawasaki) 267
4 Andrea Locatelli (Ita, Yamaha) 237
5 Axel Bassani (Ita, Ducati) 207
6 Michael Ruben Rinaldi (Ita, Ducati) 167