The Briton led every lap, finishing ahead of Edoardo Mortara, whose second-place finish moves him into a clear championship lead.
Mika Maki crashed out at the Foch chicane on the second lap, having previously squeezed between Jakes and the armco in a hair-raising start.
But Maki's misdemeanour at Foch wasn't an isolated incident, as the crane operators at Pau had a near-constant supply of wreckage to clear.
In fact, slippery conditions offline helped account for the failure of 20 out of 30 cars to make the finish.
Jon Lancaster registered his first points-finish of the year with a podium. The ART driver started 12th on the grid after a qualifying shunt, and during the race he brushed the barriers at Turn 6.
Contesting with understeer thereafter, Lancaster progressed up the order by making the most of the carnage taking place around him, as well as a fine pass for third on Franck Mailleux at the Lycee hairpin on lap 20.
The first three were covered by just over a second at the finish, but Jakes had an edge on Mortara at the crucial last corner and was able to hold his position.
"I didn't get the greatest start, but we bounced back," said Jakes after the race. "I seemed to be able to carry more speed than Maki through the first corner by taking to the outside, and then I had to stay in front.
"The race was made more difficult when the battery warning light lit up on the third lap. I wondered how long I was going to last. I was short shifting, and behind the safety car was really trying to keep the revs down low, but we came out on top and I couldn't be happier."
Mailleux settled for fourth place ahead of Christian Vietoris, who was delayed when Jean-Karl Vernay misjudged a passing manoeuvre at Lycee. Dani Clos put in an impressive showing to fight his way up from 26th on the grid to sixth place at the finish.
Classified: Pos Driver Make Time 1. James Jakes Dallara/Mercedes 41:06.198 2. Edoardo Mortara Dallara/Volkswagen + 0.662 3. Jon Lancaster Dallara/Mercedes + 1.251 4. Franck Mailleux Dallara/Volkswagen + 4.584 5. C.Vietoris Dallara/Mercedes + 6.305 6. Daniel Clos Dallara/Mercedes + 8.062 7. Michael Klein Dallara/Mercedes + 8.776 8. R.van der Zande Dallara/Mercedes + 9.769 9. Robert Wickens Dallara/Volkswagen + 10.154 10. Kazuya Oshima Dallara/Mercedes + 19.359 11. K.Tsukakoshi Dallara/Mercedes + 4 Laps 12. Richard Philippe Dallara/Mercedes + 7 Laps 13. Niall Breen Dallara/Mercedes + 8 Laps Not classified: Driver Make Laps Martin Plowman Dallara/Volkswagen 17 Erik Janis Dallara/Mercedes 17 Sam Bird Dallara/Mercedes 17 Jules Bianchi Dallara/Mercedes 16 Yann Clairay Dallara/Mercedes 11 Nico Hulkenberg Dallara/Mercedes 10 Jean-Karl Vernay Dallara/Volkswagen 9 Rodolfo Gonzalez Dallara/Mercedes 8 H.Waldschmidt Dallara/Mercedes 7 Charlie Kimball Dallara/Mercedes 6 Daniel Campos Dallara/Mercedes 5 Cheng Cong Fu Dallara/Volkswagen 3 Tom Dillmann Dallara/Mercedes 3 Maximilian Götz Dallara/Volkswagen 3 Mika Maki Dallara/Mercedes 2 Jens Klingmann Dallara/Volkswagen 1 Basil Shaaban Dallara/Mercedes 1