Members of the Citizens' Initiative Rally said they hope momentum from more than two months of street protests will carry the protest movement into electoral politics.
Campaign director Hayk Shahinyan told France's BFM TV network on Wednesday the activists want to "build a list that looks like citizens."
He said: "We have something to do in that election, like waking up the people who don't vote."
A recent poll predicted yellow vest candidates would receive as much as 13 percent of the French vote in the May 26 elections.
Weekly protests that started over fuel taxes often are ascribed to the "yellow vest" movement because participants wear roadside safety vests.
This version has been corrected to reflect Shahinyan identifies as male.