Should I protect juridically my software code?

Bonjour,
Your software "automatically" enjoys some protection from applicable copyright laws. For this reason "software as such" is not regarded as patentable invention under European patent practice, for example.
Naturally, certain technical aspects of your software may be eligible for patent protection conferred by states for their territories. This proection cannot be obtained at a file hosting service like Github.
A sensible startup will try to protect their intangible assests, i. e. crown jewels, in an optimal way.
In order to find your way, discuss your situation with a patent attorney having experience in the field of computer-implemented inventions.
So, feel free to contact me...

The question is actually whether putting the idea in a public repository and making it available to public means that it is no longer patent eligible material. Now if public is actually alpha/beta testing with signed confidentiality agreements that's a different matter but you may want to consider what deserves protection (UX, algorithm, novel concept) as there are different approaches for tradedress, secrets and inventions. Startups have different business approaches and even philosophies, some treat the app as loss leader to build up a two-sided market (if the shortage is techies), others want to keep everything secret on the server-side, others have a live-let-live approach in that the app source is available for security inspection but not generally public. It all depends ...