The launch will begin in Austria, Britain, France, Germany, Ireland, Italy, Spain, and Switzerland, The Walt Disney Company's French subsidiary said in a statement.
Other countries will be added "this summer," including Belgium, Portugal and in Scandinavia, it said.
Disney jumped into the hotly-contested streaming market with a splash last November, when it racked up 10 million subscribers within 24 hours of going live in the US, Canada, and the Netherlands.
Since then it has launched in Australia, New Zealand and Puerto Rico, with analysts estimating it now has several tens of millions of clients.
Disney is betting its extensive catalogue of kid-friendly movies, as well as the hugely popular Marvel comics and Star Wars franchises will help it elbow into a crowded market that has upended the traditional TV business model.
It has also priced its offering well below those of most rivals in its bid to sell directly to viewers, without going through third-party distributors.
Monthly subscriptions will be EUR 6.99 ($7.75) or GBP 5.99, with yearly packages for EUR 69.99 (GBP 59.99).