Exposure Metering not working on Yashica FX-3

Welcome to the forum, mathieu ...

There are several things to easily try out in order to diagnose the problem, but it's always good to know that there's a return and refund solution if in fact the camera doesn't work fully and as expected.

FX-3 meters use 3 LEDs as pass/fail type readouts in the viewfinder - a red plus and minus symbol (top and bottom), and a center green dot - and usually they'll all work or all fail. There's no test button for battery strength, but there's an exposure check button on the back of the camera that might not be marked with the original sticker. It is directly under the film wind lever, so make sure it will momentarily press and release as a proper push button in order to power up the meter and get an exposure readout.

The obvious question is whether either one or both batteries are at sufficient voltage, and the only way to be sure is to test them. Both of them should be at least close to 1.35-ish volts or better. There are no strip type testers that will work, so it means using a needle or digital tester to get something accurate to judge by. Even new batteries can sit on a shelf long enough to fail, so testing is always preferred over making assumptions.

The battery holder and cap on many of the later Yashica bodies like the FX-3 (and several of those from the Contax line) are made of molded nylon, and they have an interior contact plate of metal that has 2 'fingers' at 180 degrees on the edges to help complete the electrical circuit. The 2 batteries used (for metering only) in FX-3's can be either Alkaline or Silver Oxide types, and the Silver's are a tad more expensive, but provide for a more even current over a longer time frame. That also means they'll stay at their proper voltage longer too, so it might help to identify which type you're testing with and see if they're both the same type. LR44's are the Alkaline and SR44 are the Silver Oxide types. Having both of them as the same type helps to keep the circuit working better, and as-designed, so it might cause an issue if they're mixed and at low voltage.

Visual checks...
The 2 tabs on the metal insert of the battery cap/holder can get flattened, and when they do, they may not make full contact possible to complete the circuit. Inspect them to see if they're in shape, and if needed, you can pop in 2 good batteries and hold a piece of tin foil over them to force a proper connection just for testing purposes. If the foil works, it's likely that the metal insert isn't doing what it needs to do. It may require cleaning (cider vinegar or contact cleaners) or reshaping the tabs, or an outright replacement of the cap/holder if the tabs are broken.

Inspect the contact inside the battery compartment and if it's clean. If it's green-ish in color from a very old battery leak, or white-ish from a recent leak, it may require a thorough de-oxidation cleaning with cider vinegar. If the leak was bad enough, it may require an additional fix for the contact metal to replace what's been 'burned off'.

Repairs...
If the damage from a battery leak is bad enough, it can cause the oxidation of the copper wiring inside the camera, and there's no fix possible, other than a tear-down and replacement of the wiring itself, and/or the battery assembly in-total, when the contact is too damaged to work. This isn't an insignificant repair in terms of time/materials spent for DIY's or repair costs, so returns and refunds are the better option.

The circuit may have been fried too - or just failed due to aged components - and in that case it's usually easier and cheaper to replace the camera if internal metering is an absolute requirement - OR- use an external meter (or phone app) to provide calculations. The FX-3 is otherwise an all mechanical camera and only uses batteries for metering.

That's great news, and I'm glad you'll be able to experience the world with film. Since this could be the start of a longer journey, here's something that you might find helpful, that I put together some time ago... a new film user's guide PDF.