Let me be the devil's advocate.
There is no doubt that employees of Transavia could lose the few minutes needed to engage in detective work in various systems and retrieve archive files to check that you have indeed traveled in the past on a given flight. The info is probably stored in some archived compacted format not easily readable by the eye.
.AF agent could also lose some time trying to find your old booking. That might be easier to find, but it shows no direct proof that you actually traveled as systems are separate. I am not saying that the airline cannot do but I fully understand that they do not wish yt do this personal detective work that is costly and agent time can be put to better use. Especially for a mere 250 miles. If you were Ulti, they might do you the favor, but the rules are clear; keep your BP until miles are credited, especially on partner airlines. As I always do OLCI, I don't have that problem but it is still sometimes tough when it involves partners.