There's no guarantee that transfers between NA and EU servers will be possible, typical lack of any detailed info at the moment.

However it should be possible to get on an EU server now if you're able to try at off peak hours, the restrictions seem to be based on current server populations so all EU servers get locked at peak hours (as they were for much of the weekend) but then some generally open up to new chars at off peak hours.

(Apart from Moogle, that ones been perma locked for the last week)