Residence isn’t as simple as 183 days, although is often taken as the tipping point.
If you have your principal home in France, which you live in in a stable and regular manner (even if that means regular travel for work) and France is the centre of your economic and personal interests then you will be fiscally resident in France.
In terms of having permission to be a fiscal resident of France, your WARP card allows you to leave for up to 6 months in every year. After those 183 days you start to cross the line of no longer being fiscally resident AND lose your permission to be resident here.
However if the reason you are out of the country is that this is part of your work contract, and you have no other home, and your economic and personal interests remain in France then that is entirely different! If your self employment is a french registered auto-entreprise business, all the receipts come into a French bank account and you pay your cotisations and social charges in France as well as your income tax and remain affiliated to the French Health Service (or have full private health cover) then there is not an issue. I am presuming that the absences are not one period of 6 months, but trips here and there.
Nationality might give a bit more of a headache, as the rule of thumb is 10 months absence in the previous 5 years. Which of course can be explained away by your work. But you also have to show professional insertion and integration which is difficult if you are not here! So that might trip you up completely.
Not officially as the channel you use is determined by your passport. So people should join the non-EU channel but with a Carte de séjour your passport should not be stamped entering or exiting France. However with other countries it should be stamped as a WARP card has no validity at all outside France.
The reality is of course that this doesn’t happen!