Disneyland Paris is easiest to answer, as it's just one business. Their website states:
All major credit cards including American Express, Mastercard and Visa are accepted across Disneyland Paris including shops, restaurants, Disney Parks and Disney Village. We would recommend Euro currency for purchases at smaller food and snack stands within the Disney Parks.
Unlike in the USA, each venue in French ski resorts is typically an independent business. You should have no problem buying your lift pass or supermarket shop on card, but you might still find the odd small business on the mountain that is cash only, or one that accepts cards but is having trouble with their internet connection. Having a moderate amount of cash (e.g. €30) would cover you for that scenario.
Similar applies to service stations. Large chains on major routes will accept cards. An independent cafe in a village might be cash only.
Make sure you check what your card provider charges before using a card abroad, both for transactions and for taking cash out at a cash machine (ATM). The right card can offer a very good rate, but the wrong card could add hefty per-transaction fees that could double the price of a cheap item such as a bottle of water.