As a first step the companies are required to allow you to appeal takedowns and account suspensions/terminations (for TOS or illegal content reasons, not for non-payment reasons) for a 6 month period.
Further, if you appeal a takedown or account suspension and the company rejects your appeal, the law will allow you to take the matter to binding arbitration. If the user wins, the company pays all costs, and must reinstate the content or account. If the user loses, they only pay their portion of arbitration costs. (The company's portion are just part of doing business in the EU).
Oh and the user (not the company) get to decide which arbitrator to use, from among those that have been certified by any Member state, with the relevant expertise for the type of social network and content or TOS violation in question.
Obviously all of this is subject to change if the proposed law is changed before being enacted.