After a floodlight failure had delayed the kick-off at Ninian Park, the sparse crowd - which included Wales captain Craig Bellamy - were treated to a enthralling game of high quality.
France's Loic Remy was Wales' tormentor in chief in the first half as he twice came close to opening the deadlock.
The Lyon striker first forced Owain Fôn Williams to make a superb save to tip a fierce drive past the post, and then he saw a sublime curler fizz inches wide of the upright after again cutting in from the left flank.
Wales gave as good as they got, though, and twice saw dangerous low crosses from the right flash across the French six yard box.
But then with the half-time whistle fast approaching, Wales found the breakthrough out of nothing.
Evans showed typical determination to chase what seemed a lost cause down the right wing, but his presence forced centre-back Habib Bellaid to fluff his attempted back-pass.
Evans pounced on the loose ball just inside the box, rounded the on-rushing goalkeeper with a deft drop of the shoulder and then showed great composure to stroke the ball into the net from a tight angle.
The entertaining football from both sides continued after the break, with Wales in particular enjoying impressive periods of possession.
Remy continued to look France's most potent attacking threat, forcing Williams to save a downward header at the far post on 62 minutes.
But the best of the action was saved for the final 20 minutes as the goals arrived in a remarkable flurry.
The first came for France from the penalty spot on 72 minutes as substitute Gourcuff sent keeper Williams the wrong way after Mike Williams had pulled back Yoan Gouffran in the box.
Four minutes later, France were ahead as substitute Payet fired a glorious effort into the bottom corner from 20 yards.
But Wales, who had an average age of just 18, had plenty left in the tank.
Darcy Blake's determination enticed a clumsy challenge in the French penalty area, and Evans blasted home the resulting penalty to level.
It took only another three minutes for Wales to reclaim the lead.
Joe Jacobson's free-kick was spilled by French goalkeeper Geoffrey Jourdren, and substitute Bradley scored from the rebound after following in.
A remarkable victory was then put beyond doubt in the second minute of injury time when a foul on Simon Church gave Evans the opportunity to claim his hat-trick with another penalty.
Wales U21: Williams, Blake, Mike Williams, Ribeiro, Jacobson (capt), Ramsey (Bradley 58), Allen, MacDonald, Collison, Vokes (Church 70), Evans.
Subs Not Used: Rhys Taylor, Marc Williams, Neil Taylor, Adams, James.
Booked: Mike Williams, Owain Williams.
Goals: Evans 45, 79 pen, 91 pen, Bradley 81
France U21: Jourdren, Dabo, Kaboul (capt), Bellaid, N'Zogbia, Dia (Quercia 84), Digard, Coutadeur (Payet 50), Remy, Marveaux (Gourcuff 69), Gouffran.
Subs Not Used: Ruffier, Moutaouakil, Matuidi, Muratori.
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