After claiming an unexpected bonus point victory over Ireland last week, the extra point was in the bag by halftime as Eddie Jones's team exposed France's ragged defence again and again with a relentless deluge of kicks of every description.
The irrepressible May bagged the first three and Henry Slade the fourth as England forged a remarkable 30-8 halftime lead.
A penalty try and one for Owen Farrell put the game to bed early in the second half.
England top the standings with 10 points from two bonus-point wins, with Wales - who they face next in Cardiff - on eight after their two opening victories.
It was their second-highest margin of victory over the French, a point shy of their 37-0 win in 1911.
"When you've got a bonus point after 30 minutes, you've done pretty well but I thought our second half performance was even better," said Jones. "Our focus and discipline to keep France scoreless was outstanding."
France, who beat England in Paris a year ago, have now lost 15 of their last 19 games and have managed only two championship victories at Twickenham in 30 years.
They had no answer to England’s relentless attacks, particularly their array of kicks that had them turning, retreating and tying themselves in knots from start to finish.
"At the moment we are having a great deal of success with our kicking and if you chase well it's difficult to counter," said Jones. "If teams defend as they do now, there’s space in the back field."
QUICK OFF THE MARK
The die of England's go-to attacking tactic was cast in the opening exchanges and France failed to find any answers.
For the fifth game in a row, England had a try within the first three minutes. A mazy run and kick through by Elliot Daly set up a mismatch between some lumbering blue shirts and the quicksilver May, which England’s winger won with embarrassing ease to touch down after 67 seconds.
The second came with echoes of Jason Robinson as May stuttered and dummied to somehow create space from nothing to zip past Damian Penaud to score his second.
His third was a far easier finish after Chris Ashton joined the kicking gang, nudging a perfect grubber into the same left corner to send Twickenham wild as England led 23-8 with less than half an hour gone.
A great run by Yoann Huget sent Panaud over for France but they then immediately failed, yet again, to deal with a huge Farrell up and under and prop Kyle Sinckler spun a pass to Slade to dance over for a 30-8 halftime lead.
They stretched that with a penalty try after Gael Fickou dragged down Ashton as he bore down on another kick through by Slade and Farrell added the sixth, chasing his own kick after he took a quick tap and go on the halfway line.
England then showed terrific focus to defend their line and keep their shape amid the usual influx of replacements as France drifted to yet another defeat.
"We got spanked," said lock Arthur Iturria, summing up another day to forget a week after his team blew a 16-0 halftime lead to lose at home to Wales
Coach Jacques Brunel could not say he did not know what was coming after England had used the kick and chase with such success in Dublin last week and he will have more questions to answer after picking a back three of players all operating out of their usual positions.
"England put us under pressure throughout the game and we just could not deal with it," he said, having failed to stem the tide with the second-half introduction of uncapped fullback Thomas Ramos. "They had an excellent kicking game and continually took advantage of the space.
(Reporting by Mitch Phillips, editing by Christian Radnedge and Pritha Sarkar)
