A try by Owen Williams, converted by Alex Walker, put Wales in front in the quarter final but Fiji had levelled the score by halftime thanks to a converted try by Levai Ikanikoda.
The Fijians seized control in the second half, racing over for four unanswered tries to stroll into the semi-finals with a comfortable 33-5 victory.
The defeat saw Wales move into the Plate section where France stood in the way of making the final.
Wales got off to the perfect start when youngster Tom Habberfield touched down in the first minute. Walker again added the extras but France hit back through Terry Bouhraoua. However the same player was then sent to the sin bin to put his side a man down.
In a tight match, Richard Smith waltzed over midway through the second half. Walker's conversion proved crucial as France scored through Mathieu Acebes but Bouhraoua was unable to pull his side level with an astray conversion to give Wales a narrow 14-12 win.
In the Plate final, Wales brushed aside former series champions Samoa 26-15.
Harry Robinson and Habberfield raced over in the first half (Walker again adding the extras to both tries) to give Wales a 14-5 lead at the break.
Second half tries by Tom Prydie and Habberfield put Wales in control as Paul John's men got their campaign off to a winning start.