Brennan allegedly assaulted Ulster supporter Patrick Bamford after leaving the playing area at Stade Ernest Wallon and climbing into a seated area.
Thomas, meanwhile, is alleged to have engaged in what ERC term "aggressive exchanges with spectators" and/or "aggressively attempted to enter one of the seating areas" and/or "made an offensive hand gesture towards spectators."
While Brennan is no longer part of the Ireland set-up, Thomas remains an integral member of Wales' RBS 6 Nations plans, with their tournament opener just 10 days away.
If the complaints are proved, both players could expect a ban and fine.
ERC have also announced further investigation into the behaviour of a section of Ulster supporters, and Toulouse's alleged failure to control their players with regard to the incident.
Disciplinary hearings for Brennan and Thomas will be convened as soon as practicable.
Brennan, 33, claimed he was provoked by Ulster supporters as he warmed up with fellow Toulouse substitutes behind the posts.
Toulouse also mounted a vigorous defence of the former Dublin milkman, but Ulster claimed Brennan had tarnished rugby with his actions.
Brennan allegedly punched Bamford several times, leaving the 25-year-old accountant requiring medical treatment at the ground and on his return home to London.
Thomas, meanwhile, proved an animated bystander, but he could also pay a hefty price.
The Wales star, who is set to rejoin Cardiff later this year, missed the majority of Wales' Six Nations campaign last season after suffering a burst blood vessel in his neck, something akin to a minor stroke.
It happened just hours after he appeared on a BBC Wales television programme, defending his fellow Wales players in the wake of Mike Ruddock's shock departure as national coach.