Timatic via the Emirates website says:
Visa
Visa required.
Visa Exemptions:
Passengers with a Hayya Entry Permit (A1) (A2) (A3) or (A4) and a return/onward ticket. The permit contains a QR code for verification of the passenger and must be scanned before boarding.
Specific requirements apply:
- Hayya Entry Permit (A2) for Gulf Cooperation Council (GCC) residents: they must have a residence permit issued by a GCC country for at least 3 months and their profession must match the one stated on the permit;
- Hayya Entry Permit (A3) for Electronic Travel Authorization (ETA): they must have a residence permit or visa issued by Australia, Canada, New Zealand, USA, United Kingdom or a Schengen Member State;
- Hayya Entry Permit (A4) for companions of GCC Citizen or Resident: they must have a residence permit issued by a GCC country for at least 3 months and they must be accompanied by the sponsor or his/her first or second degree family member.
Visa Issuance:
Nationals of France with a normal passport can obtain a visa on arrival for a maximum stay of 90 days. They must travel as tourists and have:
- a return ticket; and
- a hotel reservation confirmation or address in Qatar for the duration of stay in Qatar.
Additional Information:
Visa validity can be checked at https://tinyurl.com/4ax9e6y3 .
Warning:
Visitors must have health insurance if their duration of stay is more than 30 days. They can purchase it before departure. More details can be found at https://tinyurl.com/5n8x23e3 .
The visa contains a QR code for verification of the passenger and must be scanned before boarding.
The information on the visa must match the details stated on the travel document.
(emphasis mine)
So you can either get a visa in advance, or get it on arrival. The only tricky part is the hotel reservation confirmation if you are only staying a few hours on the same day. I suppose they would waive the requirement in that case, but that needs to be checked.
Wikipedia states:
Visa exemption (free visa on arrival)
Ordinary passports
Citizens of the following countries are automatically granted a free visa upon arrival for stays up to the duration listed below. They must hold passports valid for at least six months from the date of arrival, as well as a return or onward ticket (unless if holding a valid visa issued by Oman). However, some nationalities must meet additional criteria in order to be granted the visa waiver:
90 days within any 180 days
European Union member states (except Ireland)
(...)
The official source tells us:
Free On-arrival Tourist Visa for 90 Days Non-extendable for (43) Countries
List of countries covered by this visa
(...)
France
(...)
Conditions and Requirements:
- Passport valid for at least three months
- Availability of confirmed return ticket
- Hotel reservation at any hotel in Qatar during the visit period, or a clear address of a friend or relative.
- Health insurance from an accredited insurance company
I suppose that many people would consider that a free visa-on-arrival is the same as no visa required.
