France took the lead on 18 minutes thanks to a Simon Courcoul penalty but after that it was one-way traffic with Bolwell getting the ball rolling with England's first try on 33 minutes.
Fly-half Josh Sharp converted and while Bolwell was replaced soon after, England were relentless and Tompkins dotted down four minutes before the break. Sharp again added the extras.
England picked up from where they left off after the interval and they had their third try of the match a minute into the second half, Hill getting his name on the scoresheet.
Sharp again converted but that served to stir France into life and just three minutes later they had their first try of the contest when Francois Fontaine dotted down to give the home side something to cheer.
Courcoul added the conversion and the gap was just six when winger Clement Mouraud forced his way over on 48 minutes but Sharp restored some breathing space for England with a penalty.
A try by France right winger Arthur Bonneval, 11 minutes from time, brought France to within two at 24-22 when Courcoul converted but Sharp's 66th-minute penalty ensured the hosts needed a try to pull level and to convert it for the victory but neither were forthcoming.
Meanwhile, Ireland, who finished second last year, made sure of third place with a thumping 40-0 victory over Scotland.
Prop Jeremy Loughman helped himself to two tries while scrum-half Nick McCarthy, No.8 Nick Timoney, prop Oisin Heffernan and flanker Josh Murphy all went over.
Fly-half Ross Byrne added three of the conversions while centre Fergal Cleary took on the role late on and slotted two.
Wales vented their frustration of finishing outside the top four with a comprehensive 50-0 win over Georgia, running in seven tries as prop Alex Jeffries and full-back Dafydd Howells helped themselves to doubles.
Tyler Morgan, scrum-half Tom Williams and winger Rhys Williams also got in on the act while fly-half Luke Price kicked nine points and his replacement Dan Jones booted six.
And Italy clinched seventh place, forcing Portugal down into eighth, with a hard-fought 13-7 win - replacement Yannick Agbasse securing the try that settled the contest in the final minute.