@CaptainOatFlosser as PP has already pointed out, there are two languages, Spanish and Catalan. Some people will be accomodating and talk to you in Spanish, others even in the administrative offices, library, paediatrician will totally refuse (as it is their right) to speak Spanish.
Schooling, even private , cannot be done in Spanish. Catalan only. Some bilingual private school have half Catalan Half Spanish, and then there are the international schools.
Catalan will be more dominant outside Barcelona.
Pre-school in Spain (as in the majority of continental Europe) is free, you only pay for the meals and they are quite cheap.
Health care is absolutely amazing. Kids are seen by a paediatrician as their main doctor, everything is free, and you don't have to wait long for specialist or exams.
One of the main difference for a British family might be the time distribution. Lunch is at around 1.30-2, and for many even later, and dinner after 9. You will see a lot of kids around at any time of the day or night. Kids don't go to bed as early as in UK
Shops open late in the morning and close late at night.
It is a very relaxing and enjoyable way of life. I am in Sydney right now and still Barcelona tremendously.
IMPORTANT as much as I love Barcelona, the pickpockets and bag snatchers (in cafe, beach, bus, in the stroller at a park..... anywhere and everywhere) is a massive pain you need to be aware. NEVER put a bag on the floor, behind your chair, next to you on a train, always close your bag, always have in at the front.
Once you know it, you can prevent it.
We used to be members at the beach clubs (sounds posh but actually very cheap) so we would have a locker to leave bag in.
Lucky you, Barcelona is fantastic.