BigGrecian is right. The European Aircrew Regulation Part-FCL and the accompanying EASA inspection is going to come as a huge shock to many schools. Not all of them will pass it. Similarly I wouldn't be surprised if several of them decide that it's just too painful to go through the process of compliance and give up offering a European licence.
You need to research your American school VERY carefully before deciding to part with your cash.
Start by asking them when its inspection is due. If it's already had it then ask to see their ATO certificate.