Not sure where you got this from. Coyotes can EASILY clear a 6-7 foot fence, and readily will if there is food on the other side without even blinking. And yes, a German shepherd would too. Athletic dogs are known escape artists.
As for a LGD, OP, please please do your research first. I don’t want to assume you haven’t already so don’t take this the wrong way. There’s just so many dogs who get sent from house to house because people don’t know what they’re in for. A Pyrenees is a decent choice but you have to know what they are trained to do. They will also bark.. all night long. It’s their job. If you snatch two dogs off CL and expect them to be great with the kids and perfect chicken guardians with no research, I’m afraid you will be very disappointed and frustrated very quickly.
Not trying to be insulting, please don’t be insulted haha. Dogs are just so much more of a responsibility than chickens. Maybe you know all of this, it’s hard to tell from a short forum post of course.
maybe may experiances in this area are unique. Yes, I know an athletic dog can and will jump. My parents have had a number German Shepards none of them have ever jumped a 4 foot field fencing, but they aren't trained to either. I've got the same type of 4 foot field fencing and I've never had trouble with coyotes jumping it, though I have seen them in the area. This has been my experiance and what I have seen, not saying it is right or the same experiances for everyone everywhere, heck I've only lived in one area. 
) but my neighbor shot it.
, especially that I went down to close the gate a little later than usual. Spent the rest of the night rounding them up, found 2 that ran away; Baby Rooster, a Dutch Bantam and Baby spice who's sweet but little clueless and usually last one in the coop, prob what saved her feathers.
