Unknown LED fixture replacement identification
Barking up the wrong tree.
The LED emitter is not defective
Since the beginning of artificial light, the emitting device has been a high-wear item that needs frequent replacement. We've been replacing logs, candles, wicks and bulbs for 10,000 years, so it seems perfectly reasonable that &quot;surely the light emitting thing must be frequently replaced&quot;.
You have charged headlong into this project with this assumption on your mind, and have never doubted it or re-examined it.
In similar vein, vacuum tubes in radios once needed frequent replacement.  Now, they are replaced by semiconductor transistors that essentially never fail.
That is what has happened with LED.  The &quot;light emitting thing&quot; is a semiconductor, and is vanishingly unlikely to fail.   Not impossible, but on any light assembly, it's the least likely to fail.
As such, LED light fixtures have no reason to make the 'bulb' replaceable.
The electronic driver, which conditions supply power to the exact current flow needed for the LED, is a different matter.  It is full of less reliable parts such as capacitors and Chinese 'anything'.
What you certainly have there is a perfectly functional LED and a broken driver.
But don't take my word on it. Place that lamp onto a bench power supply.  Tell the power supply to supply 10 milliamps max (better power supplies let you do this - very important).  Then increase voltage until it lights.
Don't be tempted to run it at higher milliamps unless its heat sink is properly installed. That will burn it up.
Look at the driver
I'm pretty sure France uses something like the Europlug, and not that tiny little barrel connector I see. Therefore, there is something between the little barrel socket and AC mains power.  My guess is the driver is an electrical &quot;match&quot; for that particular Cree emitter.  That, I think, is the item which has failed.
That driver module you photographed, the picture is too poorly lit and blurry to make out the figures, but it clearly says &quot;Constant Current Type&quot;.  That's very important, and also not a surprise, since it is the nature of LEDs that they must be driven in a current-regulated fashion to get peak performance out of them.  (they are unable to self-limit their current the way an incandescent can).
Anyway, any driver should suffice so long as it has

the exact current output that this driver states
An input AC mains voltage range that is acceptable
An output voltage range that is compatible with the LED emitter
The necessary government certifications (CE is worthless, but note the &quot;TUV&quot; stamp just to the left of it).