After overcoming reigning champion Ireland in its first game, England produced a dominant display that was spearheaded by wing May's treble inside the opening half an hour.
Henry Slade also went over prior to half-time, with a penalty try and Owen Farrell's score coming after the break.
While England's title credentials were strengthened with a second bonus-point win, which put it back top of the table, France saw its virtually extinguished nine days on from throwing away a 16-0 lead in a loss to Wales.
For the fifth successive match England registered a try inside the first five minutes, May racing through to dot down after Elliot Daly's measured kick in a move that would prove fruitful for Jones's men in the first half.
Two Farrell penalties were sandwiched by Morgan Parra getting France on the board before May went in again, collecting Farrell's long pass and side-stepping Damian Penaud to finish.
May completed his hat-trick as he again raced onto a kick, this time delivered by Chris Ashton once Parra misjudged a high ball.
Penaud was being targeted defensively but he did score France's only try after Yoann Huget had shaken off three would-be tacklers.
Yet England entered the interval with a 30-8 lead as Slade scored their fourth try on the stroke of half-time, with Danny Care's grubber kick turning the French defence once more.
That advantage was increased to 36 points by the hour mark as England's kicking game continued to expose French frailties.
Jones' side was awarded a 49th-minute penalty try when Gael Fickou was yellow carded for hauling down Ashton before he looked to collect Slade's kick through, while Farrell got in on the act after following in his kick when Antoine Dupont nudged the ball away from a diving May.