After both sides had missed two early penalties, Slade made no mistake with his third kick to make it 3-0 after 32 minutes, but France his straight back through scrum half Baptiste Serin to level the scores.
As half time approached, England regained the lead, Slade with his second penalty of the afternoon to make it 6-3 which brought the largely uneventful half to a close.
The hosts started the second half with real promise and put pressure on France early on. With points on offer in front of the posts, England opted for the scrum and after continued dominance the referee awarded England the penalty try, which was converted by Slade.
With 50 played, England extended the lead, Slade with his third penalty after a French infringement which also saw centre Etienne Dussartre sent to the sin-bin.
But you can never write France off, and despite being a man down, the visitors created an overlap in the corner and wing Gabriel Lacroix dived over to score, which was converted by Serin to make it 16-10.
As the game approached the final quarter. England began to reassert some authority and a mix up in the French defence gave England the put in in front of the posts, and captain Jack Clifford peeled away from the back of the scrum to dive over to make it 23-10.
With ten minutes to go Clifford scored his second try, fluid passing - including a sublime tap-pass from prop Luke Cowan-Dickie - freed up the captain to dive over. And Clifford completed his hat-trick with two minutes to play, touching down in the corner before wing Henry Purdy scored his first England try after a good pass from full back Ben Howard.
Clifford said: "We're delighted to get the win - although the full time score of 40-10 seemed a long way off at half time, when we went in 6-3 to the good. I think it's fair to say that the coaches had a few stern words with us in the changing room, but it was needed and it really geed us up to go out and perform in the second period.
"Of course from a personal point of view I'm happy to have scored three tries - particularly as all of my family were in the crowd - but as captain it was the performance I was most pleased with. We got on to the front foot in second half and never really looked back. I'm not sure if the French tired but we definitely exploited a few gaps in the last ten minutes and got some good points on the board."
Points: Penalty Try 1, Clifford 3T, Purdy 1T; Slade 3P, 3C.
England Under 20 starting XV v France
15 Ben Howard (Worcester Warriors)
14 Jack Arnott (Exeter Chiefs)
13 Mark Jennings (Sale Sharks)
12 Sam Hill (Exeter Chiefs)
11 Henry Purdy (Leicester Tigers)
10 Henry Slade (Exeter Chiefs)
9 Alex Day (Northampton Saints)
1 Luke Cowan-Dickie (Exeter Chiefs)
2 Nathan Morris (London Wasps)
3 Kyle Sinckler (Harlequins)
4 Elliott Stooke (Gloucester Rugby)
5 Dom Barrow (Leeds Carnegie)
6 Harry Wells (Leicester Tigers)
7 Joel Conlon (Exeter Chiefs)
8 Jack Clifford (Harlequins) (c)
16 Danny Herriott (Northampton Saints) on for Harry Wells 75 mins
17 Danny Hobbs-Awoyemi (Northampton Saints) on for Nathan Morris 71 mins
18 Scott Wilson (Newcastle Falcons) on for Kyle Sincker 60 mins
19 Tom Jubb (Saracens) on for Dom Barrow 66 mins
20 David Sisi (London Irish) on for Joel Conlon 52 mins
21 Callum Braley (Bristol Rugby) on for Alex Day 52 mins
22 Ollie Devoto (Bath Rugby) on for Jack Arnott 42 mins
23 Tom Stephenson (Northampton Saints) on for Sam Hill 71 mins