International Internship Programme (VIE) is a type of contract that offers to many European citizens to work abroad. From the program description, you are officially employed by the French Ministry of Foreign Affairs.
French people have to file their tax in France, as afar as I understood, but what about non-French citizens? Should they file in France, in the host country or citizenship country? If that matters, let's take Germany as the citizenship country.
According to the program website
The V.I.E has a public status. He / She comes under the protection of the French Embassy in the country of assignment and has no contractual link with the French company benefiting from the assignment. He / She receives a fixed living allowance (paid into a bank account in France) which varies according to the country where the assignment is carried out and is generally not subject to payment of contributions or taxes in France (except for specific host countries which have certain conditions).
(Emphasis mine.)
While a program coordinator at Ubifrance (the French agency for export promotion) will have more specifics, it is a safe bet to say that you are not responsible for taxes to France. The same information sheet is provided by the French Consul in Atlanta, Georgia, USA and contains the same statement.
In the case of a German citizen, according to this website from the European Union, if you are not "tax resident" in Germany (present in Germany for 6+ mo in a year) then you are not taxed on income earned outside of Germany.
This creates the interesting situation of not being taxed anywhere on income from VIE income. This is in line with the goals of the VIE program and the charter of Ubifrance to help French businesses abroad.
