England started brightly and wing Howard Packman made a strong break out wide but the French scrambled back to bundle the Northampton Saints man into touch.
It was France who got the first points on the board with a well taken penalty out wide, but England silenced the partisan crowd when Bolwell touched down a driving maul from a line-out to make it 7-3 after Sharp's conversion.
England had thought they scored before that when wing Tom Fowlie looked to have legitimately touched down in the corner but the referee judged the ball not to have been grounded.
As the half came to a close England had a deserved second try, a strong break from hooker Jack Walker was offloaded to Tompkins who showed impressive strength to hold off two defenders before touching down.
Visitors England started the second half well and Hill scored a memorable try, picking up the ball in his own half before beating three French defenders and diving over to make it 21-3.
This acted as something of a wake up call to France who scored two quick-fire tries to make the score 21-15 and a six-point game.
A Sharp penalty after 57 minutes made it 24-15, but a third French try reduced the deficit to just two points at 24-22.
Sharp's second penalty with ten minutes to play gave Head Coach John Fletcher's side a five-point cushion at 27-22 and that's how it stayed until the final whistle.
Captain James Chisholm was delighted to get the win, he said: "We really had to work for that and full credit to France, at 21-3 up we let them back into it, but there's a real determination in this group and there was no way we were going to let that lead slip through our fingers once we had it."
Head Coach Fletcher added: "I'm delighted for all of the guys, it was a great game and both sides played their part - I thought we played well for large periods and deserved to get the win. Full respect to France though, they had the crowd behind them and pushed us all the way."
Points: Bolwell 1T, Tompkins 1T, Hill 1T; Sharp 3C, 2P
England Under 18 starting XV against France
15 Howard Packman (Northampton Saints & Moulton College)
14 Tom Howe (London Wasps & Shiplake College)
13 Nick Tompkins (Saracens & Oaklands College)
12 Rory Jennings (Bath Rugby & Bryanston School)
11 Tom Fowlie (London Irish & St Pauls Catholic College)
10 Josh Sharp (Saracens & Oaklands College)
9 Stuart Townsend (Exeter Chiefs & Ivybridge College)
1 Luke Chapman (Exeter Chiefs & Truro College)
2 Jack Walker (Leeds Carnegie & Prince Henry's Grammar)
3 Paul Hill (Leeds Carnegie & Prince Henry's Grammar)
4 Jordan Onojaife (Northampton Saints & Stowe School)
5 Charlie Ewels (Bath Rugby & Bryanston School)
6 Matt Bolwell (Exeter Chiefs & Truro College)
7 Andrew Boyce (Worcester Warriors & Kings Worcester)
8 James Chisholm (Harlequins & Brighton College) (c)
16 Sam James (Saracens & Bishops Stortford)
17 Neale Farthing (Leicester Tigers & Wyggeston & Queen Elizabeth College)
18 Lewis Boyce (Leeds Carnegie & Prince Henry's Grammar)
19 Charlie Hewitt (Exeter Chiefs & Ivybridge College) on for Charlie Ewels 35 mins
20 Josh Peters (Northampton Saints & Oundle School) on for Jordan Onojaife 46 mins
21 James Mitchell (Sale Sharks & Lymm School) on for Stuart Townsend 50 mins
22 Josh Skelcey (Northampton Saints & Moulton College) on for Tom Howe 50 mins
23 Louis Clayton-Molloy (London Wasps & Harrow School)
24 Andrew Hughes (Sale Sharks & Hartpury College) on for Andrew Boyce 35 mins
25 George Perkins (Saracens & Oaklands)