Hadrien

You say your XR500 was in AP mode, was it behind another router and is it still?. There is some sort of port conflict going on which is why I suggested a DMZ as I know from checking that the HUE uses standard port 80 to access the internet. I suggest using UPnP and 1 router only unless you are familiar in vlans or know how to setup different subnets. 

have you contacted their tech support or looked on their site to find out which port or range of ports your hue uses? You could try inputting the ip address of the hue that the XR500 assignes into the XR500 DMZ and see if it works then ( a reboot of the hue maybe required after this). This would indicate a port issue. I would assigne a static ip address to the hue beforehand.  

Hello !
I didn't contact their support yet but already looked on their website/forum and I didn't find a solution...
I assigned a static IP to the bridge too, but I will try the DMZ assignation. Thanks for this suggestion !
I will revert to you after testing.
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I put it in DMZ but nothing happen

Hello !
I didn't contact their support yet but already looked on their website/forum and I didn't find a solution...
I assigned a static IP to the bridge too, but I will try the DMZ assignation. Thanks for this suggestion !
I will revert to you after testing.
----
I put it in DMZ but nothing happen