If you've boosted your character to 70 then you will need to complete your MSQ to get to the locations the level-appropriate FATE's are located (as they will be locked behind quests within that).

However, all FATEs allow you to level sync so just enter the Blue Circle indicating the FATE proiximity on your Mini Map and you'll get an option to Level Sync - this will bring your level down to the level of the FATE. You'll earn Exp, Gil and Seals accordingly upon completion based on the FATE level.