Great Pyrenees tend to have a calm and patient nature. Although they are a serious, focused, and independent working dog, they often have a sweet, gentle, and affectionate personality with their families.
They tend to get along well with children and other pets and tend to take on a guardian role. Their protective instinct makes them wary of strangers, but they will open up once introduced as long as they have been properly socialized.
If the other parent breed has a similar temperament, then you should be able to expect something similar from a Great Pyrenees Mix. In addition to talking to the breeder about the other parent breed, you can also meet the mother in person.
This allows you to see what her temperament is like and what behavior she is modeling for her puppies. The breeder should have started some socialization and training, but it is up to you to continue to train and socialize a puppy once you get them home.