Tigers trio Tom Collett, Ben Youngs and Greig Tonks started the game, with club colleague Jack Cobden on the bench as England staged a spirited second-half comeback to secure the win.
England trailed 5-0 at half-time, but they came good in the second half and a 71st-minute try by replacement Mike Stanley stole the victory.
Prop Yvan Watremez came off the back of a driving maul to give France the lead with the first try of the game but England stayed in contention with some good work in the line-out, while scrum-half Youngs marshalled the pack well.
A 42nd-minute penalty by Rob Miller earned England's first points and they took the lead soon afterwards with a second successful penalty.
France regained control when replacement fly-half Pierre Bernard scored a drop-goal on 66 minutes but then it was England's turn to take the initiative.
After just four minutes on the pitch, Saracens winger Stanley made an impression when Collett, enjoying a superb game, stole possession from a French clearance kick. Collett showed an impressive turn of speed to break through the midfield and off-loaded for Miller to set up Stanley on the right and he charged through to score.
England head coach Chris Kibble said: "I'm very happy with this win, especially considering this is our first international of the season. That will lift our spirits tremendously.
"It was nice to score a good, fluid try at the end of the game because that was something we had been lacking. Carl Ferns led by example and Tom Collett had a great game at hooker."
England's next game is against Scotland at Burnbrae on Sunday, April 8.
15 Greig Tonks (Nottingham High & Leicester Tigers)
14 Sebastian Stegmann (Cranleigh School & NEC Harlequins)
13 Ben Williams (Bryanston School & Bath Rugby)
12 Luke Eves (Colston's Collegiate & Bristol Rugby)
11 Charlie Sharples (St Peters & Gloucester Rugby)
10 Rob Miller (Keswick School & Newcastle Falcons)
9 Ben Youngs (Leicester Tigers)
1 Ben Moon (Ivybridge Community College & SWERA)
2 Tom Collett (Wyggeston & QEI College & Leicester Tigers)
3 James Currie (Millfield & Bath Rugby)
4 Graham Kitchener (Adams Grammar & Worcester Warriors)
5 Dan Williams (Ivybridge Community College & SWERA)
6 Calum Clark (Barnard Castle & Leeds Tykes)
7 Jacob Rowan (Bradford Grammar & Leeds Tykes)
8 Carl Fearns (capt) (Sedbergh & Sale Sharks)
16 Alex Brown (Dulwich College & Saracens)
17 James Clark (London Irish)
18 Joseph Marler (Sussex Downs & NEC Harlequins)
19 Courtney Lawes (Moulton College & Northampton Saints)
20 Tom Sargeant (Royal Grammar Guildford & NEC Harlequins)
21 Mike Macfarlane (Royal Grammar Guildford)
22 David Lewis (Ivybridge Community College & SWERA)
23 Mark Davies (St Peters High & Gloucester Rugby)
24 Jack Cobden (Wyggeston & QEI College & Leicester Tigers)
25 Mike Stanley (Oaklands College & Saracens)
26 Henry Trinder (Hartpury College & Gloucester Rugby)
* Leicester lock Gregor Gillanders played his part from the bench as England U-19s beat their French counterparts 29-5 at Henley.
Captain Hugo Ellis scored a hat-trick of tries as England completed their preparations for the IRB U-19 World Championships where they face pool games against Samoa, Argentina and New Zealand.
Scrum-half Joe Simpson and full-back Alex Goode, who also added two conversions, were England's other try-scorers.