With both kickers missing the conversions, the scores were tied at five-all at the break, and once again it was the French youngsters who scored first, taking a 10-5 lead in the 20th minute of the second half.
However, Wales hit back through full back Aaron Bramwell not seven minutes later for the scores to remain level at 10-10.
Both teams worked hard for the clinching score as the clock ticked down, and it was replacement Thibaud Duvallet's drop goal on the stroke of full time that settled the game in France's favour.
Summin up Wales's disappointment, Captain Jonathan Spratt said: "We are really disappointed that we lost this final game of the tournament. With the scores level towards the end, we didn't do enough."
Wales 10 - France 13
Tries: Charles Platek (2)
Drop-goal: Thibaud Duvallet
Tries: William Rhys Jones, Aaron Bramwell