Why are the in-flight refueling probes of French-built fighter aircraft non-retractable?
According to Dassault, this configuration was chosen in order to reduce complexity and therefore avoid deployment/retraction problems:

Failure-prone systems have been eliminated early on in the design process:
... and the refuelling probe is fixed in order to avoid any deployment or retraction problem.

There are some other advantages as well:

A non retractable probe takes up less space in the forward fuselage (where space is at a premium) compared to the retractable one. For example, when the F-16 was fitted with a retractable probe (Conformal Air Refueling Tanker/System (CARTS)) for the Indian MMRCA competition, it had to be done via a change to the forward section of the right conformal fuel tank.


Modifications for retractable probe in F-16; Lockheed Martin photo , image from f-16.net
Another good example for this is the French Mirage F1s supplied to Libya, which had their radars removed to accommodate the retractable probes and the Mirage F1C-200 version, which necessitated the lengthening of the fuselage to accommodate the (non-retractable) probe.
The French aircraft, especially the Rafale are not exactly known for their large noses. in such cases, it is better to have a fixed probe, thereby saving the space required for the deployment/retraction mechanism.

It weighs less as the system is simpler- basically, you are eliminating the deployment/retraction system of the probe.

This system offers increased fuel flow and reduces maintenance requirements.

One thing to note is that the Mirage 2000's refueling probes are removable (it appears like Rafale's too is removable), so the drag penalty is not there when the mission doesn't call for it. At the same time, this reduces the weight penalty. Interestingly, it means that the number of probes can be less than that of the aircraft itself, with the probes installed as per requirement.

Another thing is the French doctrine- Unlike US, the Armée de l'Air  doesn't put too much into mid air refueling or stealth requirements.


It can also be interpreted as a design choice- all the French aircraft, right from Mirage F1 have had fixed refueling probes (while some were modified to accept retractable ones).