In FFXIV there a few ways to relive the main story. First of all there is a housing item called The Unending Journey that allows you to replay every cut scene in the game. You can access it in every inn room in the adventures guilds in the main cities or you can craft or buy it for your own house or FC estate.
With New game+, found in the main menu under main commands /duty, you can replay all the quests you already finished. So if you fancy a do over or if you were naughty before and bought a Tales of Adventure potion to skip (part of) the story line, all you have to do is enter game+.
If you rather want a recap: here are a few video’s from Comicstorian that do just that. These are recaps from A realm Reborn (2.0), Heavensward (3.0) and Stormblood (4.0). As there is no potion (yet?) to skip Shadowbringers (5.0), there a no recaps for it yet.