Public transport options between Paris and EuroDisney

We're based in the UK, trying to arrange a family holiday for next year where everyone can enjoy themselves. So, a few days at Eurodisney and a few days in the city of Paris.

We don't want to stay on site at the theme park - too expensive, and would mean relocating to the city. We also don't really want a hotel - we'd rather have a self-catering cottage of some kind.

We also don't want to take the car. So we'll be reliant on public transport.

My knowledge of the local geography is zero, and I can't seem to find much out with google - search results focus on "official" accommodation or mass-booking sites, with very little helpful information.

So here's the question: what towns or villages should I be looking at to find self-catering accommodation where it is easy to get on a train or bus into both the city of Paris and Eurodisney? Bonus points if you can tell me the travel times. Big bonus points if you can find me somewhere to stay :)