Your tester unfortunately is mistaken. The exemption which came into force in February this year relates to all cars with Carte Grise Collection first registered before 1/1/1960. Later cars still have to have the 5 yearly test.
If there is an insurance requirement that's a private matter between the owner and the insurer and in any case it's voluntary. My classic insurer certainly has made no contact regarding this.
If you need documentary proof there is a link to the legislation on the FFVE.fr website.
Are you sure that it is the wheel bearings and not axle eye wear/elongation. Your king pin and bearings may be perfect but the eye in the beam may be out of shape ( a common problem with Austin Sevens)
Turned up for the CT this AM, and the tester was surprised to see me. He checked the docs and as Reckless said. No requirement for the test as it was pre '60 and a "light Vehicle". It was his boss that had said the test was required. So I went home with a smile having saved 59 euro - then my wife said the dish washer had packed up. On inspection, the computer was burned out and as it was over 12 years old, so it was off to buy another one. Some you win and some you loose.