Will there be problems with this?

[squashedbanana]

I have a trip coming up where I will be getting a one way flight to France, meeting up with my parents and travelling back via Eurostar. We won't be booking the return trip until we are all in France. I will be travelling with my child, the father is not on the birth certificate and he has no parental responsibility. I've been told by a friend that it could look like I was taking my child out the country permanently as when we leave we will have no return trip booked, should I get written permission from the father to cover myself even though he doesn't have PR?

No, why should you? He has no legal rights in respect of your child. Whether it 'looks' like you're permanantyly removing him/her from the country or not is irrelevant. It's what you are actually doing that is what's relevant.

Just get on the train, have a lovely time and i'm sure you'll be back home soon! And don't worry.

As the father does not have PR you do not need his consent to take your child out of the country regardless of whether you are going temporarily or permanently.