Sorry, I didn't reread the thread properly and you didn't make your situation clear in your previous post, but David has just pointed out that you are registered as an AE. So, as I think has been said, your route to healthcare is via RSI and it's not clear why you would be going to CPAM because you are not their responsibility (I assume that when you say your 'local public health bureau' you mean CPAM?). The organisation that is responsible for providing your healthcare depends entirely on your personal circumstances; in France there is not one single public healthcare provider that deals with everybody living in France, there are different providers according to your personal situation, each with their own remit and their own budget. If your personal situation is that you are registered self employed then you are the responsibility of RSI, via URSSAF.
Income tax and healthcare cotisations are two completely separate things. The tax office doesn't interfer in CPAM, RSI or any other caisse.