In XY, you can obtain the Helix Fossil randomly by using Rock Smash in Glittering Cave. However, it is exclusive to Pokémon Y. If you want it in X you will have to trade for it. Furthermore, it can only be obtained after defeating the Elite 4 and Champion.
You can obtain all other fossil Pokémon via this method, with the exception of Tyrunt and Amaura. Only Aerodactyl can be obtained pre-E4. Afterwards you can get them all. Kabuto and Omanyte are exclusive to Y and Anorith and Lileep are exclusive to X.