Never watched more than half of an episode of Eureka (and that was only the pretty bits with Michael Shanks in 'em) so I can't say for certain, however I'm pretty sure it is "free rein".

The origins of the expression, if I'm not mistaken, refer to a horse being given "free rein" to go wherever it well--that is, the horse not being held in check or directed by the use of said reins. After all, when you "rein in" something, you are holding it back from doing what it will.