Which legal documentation do I need to launch a startup?

It depends on how you want to set up your start-up company. As a corporation/partnership/sole-propietorship etc.
you need to look at the available business forms in the French Jurisdiction and decide which one will suit your business needs best from a cost perspective (what it costs to set it up and run it) and from a financial& tax perspective. They all have advantages and disadvantages that make some more suitable and more advisable to different circumstances.
If you want to incorporate your start up business then you will need to obtain Articles of Incorporation and register it with the local business registration office. The Articles of Incorporation/Partnership Agreements etc. can be drafted by a lawyer (for a higher price) or they may be obtained cheaper if you inquire around, maybe even the registration office can guide you.
You may also need to register it with the local tax authorities so you can file your tax business tax returns. Usually the tax registration does not cost anything, but not sure if in France it does.