To restart you game in Pokémon X and Y, hold down Up + B + X when your on the Pokémon X or Y title menu.
For more help, click this video here.
Hope I helped :)
During either the pre-game video or the main screen, press Up+B+X.
Some guy doing it on Youtube.
The easy way: Press new game
The hard way: I forgot... :P
Hope this helps!