Ethan Lewis crossed for a late converted try for Wales, adding to Ethan Davies' early penalty, but it's the French who are now the only unbeaten side in the competition.
"We learnt some harsh lessons, we were outplayed in almost every aspect of the game," said Wales head coach Hayward, who was not helped by yellow cards to backs Steffan Evans and Dafydd Howells.
"There is plenty to work on before we play England in a fortnight - we will have to be honest with ourselves and each other and accept we made mistakes in order to improve individually and collectively.
"We have said from the outset the Six Nations was an important opportunity to expose players to this level of rugby in order to see what they are capable of and develop them into better players.
"There's nothing better than tough international matches for doing just that and we knew this match and England in two weeks would be the biggest challenges. After these matches we will have a great idea as to where we stand in our preparation for the Junior World Championship."
With the conditions keeping running rugby to a minimum in Colwyn Bay, the two sides had gone into the break level at 3-3. But in the second half, a close-range effort from French lock Jean-Baptiste Singer, converted by Serin, proved crucial. The scrum half, who controlled the game with his kicking, added two more penalties to render Lewis' late effort a consolation.
Wales Under 20 prop Nicky Thomas said: "The boys are down but we've all come to the general consensus we need to pick ourselves back up now.
"We've got a week's rest so we can train hard for the England game, make sure our heads aren't down, and go through all our analysis and review.
"Moving forward we have to go back to basics, go back to our structure. We made vital mistakes against France and need to be more clinical.
"We need to keep a positive attitude going into the England game and keep our emotion intact. It's the first game you look for on the fixture list and emotions will be riding high."