How to handle seeing someone online claiming to be a pilot or pilot in training, who one feels shouldn't be flying, in the EU?
In general, one wouldn't.

If the user in question has never touched the yoke, there is no issue - it's not illegal to lie on the internet. 
If they're in training, it's on their instructor to set them right.

This leaves the case where they do hold a current license. Presumably you want to notify the local aviation authority that they might not satisfy its requirements.

Now put yourself in the local FAA-equivalent's shoes. Supposedly a certified pilot has posted on the internet that the artificial horizon is a lie and one should always trust their gut over it. What recourse, exactly, do you have against them? They're not under any obligation to teach flying to the general public, and there's no regulations or prescribed penalties for publishing incorrect information on the internet. 

NB: It would be very different had they identified themselves as a commercial pilot for a specific carrier. In that case, they'd be presenting their airline in a bad light, and the freedom of employment (in the US, varies in the EU) would allow their employer to take action to protect their reputation.  

A PPL, OTOH, is a more exclusive cousin to the driver's license, and merely indicates that its holder has at some point convinced their instructor that they were capable of flying at that moment, while meeting a number of formal requirements, and has renewed it since at required intervals.

The forum's administration might want to take action to keep false information away from their board, if you inform them, but interaction with them is a subject far removed from aviation.