The Ghost Girl is most likely an Easter Egg put in by Nintendo. The Ghost Girl has appeared in past generation games- Gen 4, Gen 5, and Gen 6 (This gen). Since this happened, most people think this is an Easter Egg. It may just be there to creep people out. Now for this Gen (#6), several people think that the Ghost Girl in Lumiose City has something to do with Hoopa, an event exclusive Pokemon that hasn't been officially revealed yet, but has appeared in the XY games from hacking. Hoopa is a Ghost-Psychic type Pokemon. The Ghost Girl is a ghost. Strange huh? NOT
TL;DR: The Ghost Girl is an Easter Egg put in by Nintendo, and may have something to do with Hoopa.