Intended to come back and answer this at the weekend, but was busy with family stuff on Sunday, while Monday was a working day for me (and proved quite a tough one).
Yes, he meant EU law and specifically competition law. EU competition law states that a restriction on competition can be treated as allowable if it can be shown to give rise to benefits to consumers which outweigh any restrictions of competition.
IIRC, he managed to secure an agreement from the relevant directorate of the European Commission that the rules did give rise to such benefits and, as I recall, there was also a statement that sport in general should be treated as a special case as compared with other economic sectors. This is something sporting bodies often argue, but with wildly varying degrees of merit IMO.
But the thing is that the Commission is an enforcement body. While statements to the above effect were no doubt useful for Platini, the ultimate decision as to what does and doesn't breach EU law lies with the Court of Justice, so the Commission's consent was no guarantee UEFA would prevail if the matter were litigated. There were some challenges working their way through the system, but to be honest I didn't follow what happened to them.
In terms of someone litigating in an individual country whose FA is a member of UEFA to have UEFA regulations declared unlawful in that state, I think that would be of limited value. They'd simply exclude the litigant in question, or all clubs from that country if the FA were supporting the challenge.
It's hard to see UEFA seeing too much of a problem in a legal challenge in most non-EU states, whereas obviously the heft of the EU would give them serious problems of its courts made an adverse ruling. IMO, they'd think they could ride out an adverse ruling even in post-Brexit Britain, where currently the most lucrative domestic league is played,