The tax system is based on the principle of territoriality: if you earn money in France, you have to pay tax over there.
In order to avoid double taxation, France has many agreements with foreigner countries.
For EU citizens: if you are a permanent resident, you have to declare and pay tax in France and you will not depend anymore of your foreign state.
If you decide to do not stay in France as a permanent resident, you will have the possibility to use the most interesting system for you. You can declare your income in your France and pay tax over there, or you can choose to declare it in France and profits of the following advantage and deduct this amount to your tax in your country.
For non-EU citizens: the rules are the same depending to your resident status, but the legislation of tax could change. It means that if you come from a country where France does not have agreement, you may be subject at a double taxation. In this way, you will have to declare your income in France as foreigner income to your mother country.
For workers send by their company, the French system gives them the profits of a reduced taxation ratio and the previous advantage system.
While, if you want to set up a business in France, you will be submitting as French companies at the taxation system.
French Tax System more (only French)