From what I know (thats not much ) they are good with animals around. My friend has a farm with goats pigs chickens and cats and she has 2 of these dogs and as far as I know she hasnt ever had a problem. Id like to know more to hopefully somone else will know more.
We have a Pyrenese/Bernese mix, not the brightest but loving. She isn't good with animals other than dogs who can handle her, (and our purebred bernese was complete opposite she'd hatch your chicken eggs for you)but she tries to herd the kids. Or did before, and that's a pyrenese thing so maybe they are meant to be good with animals.
Pyrs are guardians so they are good with animals and people who are "theirs", but they will defend their family and livestock to the death, if necessary. Their job is to guard livestock from wildlife like coyotes and cougars, etc. If not fenced in, Pyrs will roam as far as they think their territory is. As pets, they shouldn't be off leash and need to be well socialized with people and other pets. This site has a terrific forum for asking about the breed, http://www.greatpyr.com/forum/index.php
We have two right now....these two make our third and fourth....one of the two we just rescued, not 100% sure that he is pure but he sure looks the part and acts the part...I love them more than you can imagine...I dont use mine for guarding livestock...mine are house dogs so their job is to guard the house and us and they do an awesome job!!!! They just have lots of hair and I am not one for shaving them....they need that hair!!!!