I've looked inside your French Thread, and there the "RecalBox-Team" suggest that your Problem lies within your Powersource.
I find the very strange, because like you wrote, other Software worked on the Pi with your actual Powersource.
If I get it right from your French Thread, you’ve downloaded the Raspberry Pi Imager and let this Software choose then right RecalBox-Software and let it install it.
Maybe there is a Problem and you should try this:
Go here (French Version)
https://www.recalbox.com/fr/download/stable/rpi/rpi3/
and scroll down till you see
"Alternative : installer une image telechargee"
Klick on it
and on the next Page download and save the Raspberry Pi 3 Image on your HDD by clicking
"TELECHARGER RECALBOY POUR RASPBERRY PI 3 (8.1.1-ELECTRON)
in the green Box on the right side.
Then use the Raspberry Pi Imager to write the downloaded File (recalbox-rpi3.img.xz) onto your SD-Card.
Instead of the Raspberry Pi Imager you can use the Win32 Disk Imager
https://sourceforge.net/projects/win32diskimager/
This works without Problems for me, maybe you have to unpack the recalbox-rpi3.img.xz File to get an "IMG"-File