Lost in France, King in India

I'm not sure if this is the right place to ask this (if it isn't please move it to the correct slot on the board).

There is a line of Bourbons of Bhopal, India. However, one source says that they are descended from a bastard son of the Connetable de Bourbon, Charles III. Another source says they descend from "a secret son" he had by his wife, Suzanne de Bourbon, daughter of Anne de France, Vicomtesse de Thouars.

Now, I am confused, since why would a legitimate child be kept secret? And then, with France being as strict about legitimacy of blood they were, why wasn't this guy - Jean Philippe de Bourbon (d. 1560) - or his son crowned king instead of the Protestant Henri IV?
 
With this not being in the right forum given, I do not think France would have allowed a bastard line to be crowned. The idea of a secret son goes back to the myth of the man in the iron mask bei g Louis XIV's twin brother. Or at least to our modern eyes. I am sure there are lots of myths and fables of long lost heirs being kept away from their rightful thrones.
 
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