There are a few ATMs scattered throughout both Disney parks, so if you'd prefer to collect some extra Euros in cash rather than pay by card at shops and restaurants, the choice is there.
The machines accept all the regular cards you'd expect — both credit and debit — including Visa, Maestro, MasterCard and American Express. Those in the parks are operated by Crédit Mutuel.
If you're visiting from the UK, bear in mind that most card transactions and cash wthdrawals abroad will incur a small fee unless your bank has explicitly advertised otherwise. Though not much, it can add up over several days. Rather than withdrawing large amounts of cash, consider applying for a "free withdrawals" card to use only whilst you're away, also allowing you to keep a cap on your spending.
Cashpoints are also available at these locations:
You'll also find numerous cash dispeners around Val d'Europe Shopping Centre.