The teams had produced an 80-point thriller in the RBS 6 Nations with England winning 47-33 but this clash was never going to be as open.
France lead after 40 minutes with Jean Marc Doussain landing two penalties, either side of Burns' first three pointer.
But England improved after the break with Mapletoft making three key changes and they wrestled the initiative once Remi Lamerat was sin-binned for an off-the-ball tackle on Charlie Matthews and Burns slotted the penalty to level.
Two minutes later England were in front when Gibson finished off a free-flowing move that involved Tom Homer and Burns.
The normally reliable Homer then fluffed two penalty attempts with Doussain also missing before Clegg's drop extended the lead.
Gilles Bosch cut the gap soon after but Burns' third penalty two minutes from time clinched the win.
Wales' hopes of a place in the last four were ended in emphatic fashion buy holders New Zealand, who won 43-10 in Santa Fe.
The Baby Blacks effectively had the win sealed in the opening 36 minutes with four tries to make it 13 wins on the trot in the Under-20 competition and now they face South Africa in the other semi-final.
Hooker Rhys Williams grabbed a consolation try after the break but that was as good as it got for Phil Davies' side, who will now face Argentina in the fifth place semi-final.
Scotland's 27-3 win over Tonga in group C means they will meet again in the ninth place semi-final.
Tries from John Kennedy, Michael Maltman and captain Stuart McInally plus 12 points from the boot of fly-half Duncan Weir earned the Scots the convincing win.
Ireland will face Samoa in the other ninth place semi-final after slipping to their third successive defeat in the group stages - hosts Argentina seeing them off 24-21.