How do we know what those fundamental rights are? By observing what happens to societies that have various formulations of rights. The societies that thrive are closer to the mark than societies that are mired in misery, despair, and death.
I'll give you three: Life, Liberty, and the Pursuit of Happiness.
Death is also part of our innate nature, but you did not mention that one.
Bushido (or the form of it on Wikipedia) has a fairly different and also interesting set.
Anton LaVey (Church of Satan) has an interesting, albeit stereotypically American, eleven.
The philosophers in this list seem to focus on commandments of rationality more than morality, but that’s not something I find hugely surprising: https://en.wikipedia.org/wiki/Alternatives_to_the_Ten_Comman...
These are not rights.