The incident happened on Wednesday afternoon in the small village of Le Castellet, near Manosque.
The two Rafale aircraft had taken off from a nearby air base on a low-altitude training flight, reports say.
An investigation has been opened into the “rare incident”.
“It went so low that it made a hell of a din, I then looked up and saw the second aircraft,” the village’s mayor told local news outlet France Bleu (in French).
“It was so low that I said to myself: it went under the power lines,” Benoît Gouin, who was driving at the time, said.
The fall of the cables caused a fire which was quickly brought under control, La Provence newspaper reports.
The village remained without power for a few hours, while the access road to it was also barred for security reasons.
“There were no casualties. This in-flight incident forced the pilot of the aircraft to land safely at 14:11 [13:11 GMT]” at the Orange air base, a French air force spokesperson told La Provence newspaper. They “deplore this extremely rare incident”.
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