The European Commission has also proposed that the programming must be given "good visibility". A raft of proposals unveiled on Wednesday mean that the new wave of digital and on-demand and streaming services would have to adhere to the same, or similar, commitments that traditional TV broadcasters are forced to follow in Europe.
The Commission wants TV broadcasters to continue to dedicate at least half of viewing time to European works and will oblige on demand providers to ensure that they have at least a 20 per cent share of European content in their catalogues.
"These percentages are not going to represent a major effort," said Günther Oettinger, the Commissioner responsible for Europe's digital single market. "We are providing a certain degree of security for the European film industry."
The German official told a news conference in Brussels said the proposal would have a "positive impact on cultural diversity and bring more opportunities for European creators."
He added, "This is also all about trying to create a European identity."
"The way we watch TV or videos may change, but our values don't," he added.
But Paul Nuttall, UKIP deputy leader, criticised the quota system, telling this website, "This is just regulation for regulation's sake. Netflix themselves have said that they are pushing more and more 'home-grown' material without this regulation so why on earth is the EU getting involved?"
"Millions of British people have managed to enjoy Netflix and other streaming services perfectly well up until now and I'm sure the percentage of 'European content' will matter very little to people wanting to relax after work and enjoy some television, European or otherwise."
For television, the new proposals would boost the powers of audiovisual regulators, making sure they are independent from government and industry, and give broadcasters new flexibility in the way they screen advertising.
The Commission says there are cultural benefits to the move, which would affect Netflix and Amazon Prime Video.
Fighting the dominance of Hollywood is a major priority for France, which has for years subsidised its own national film industry through a special tax on privately owned broadcasters that rely heavily on US-made content.
In addition, the EU hopes to tax US web streamers in order to help fund European movies and TV shows.
According to a study provided by the Commission, Netflix already devote 21 per cent of their film catalogue to content from the EU.
The call for quotas is part of a proposed update to the EU's audiovisual media services directive.
Other measures include a requirement that video-sharing platforms including YouTube adopt "better" measures to protect minors from violent content and people of all ages from clips that act as an incitement to hatred.
The proposals also include a call for the creation of new symbols or phrases that would warn viewers of potentially harmful video content - such as bad language, sex or drugs - that would be used across the EU by both broadcasters and internet-based platforms
The Commission also says TV broadcasters should have more flexibility as to when they show adverts.
It is the demand for quotas, though, that has attracted most reaction.
Alice Enders, from the media consultancy Enders Analysis, said the decision to table the proposals was "driven by the core problem that the EU identified 40 years ago, that the Hollywood studios and other US producers dominate global box office and broadcasting because they have scale that cannot be achieved in a fragmented EU."
"It does send out an important signal to Netflix and others.
"But let's face it, the online services could meet the 20 per cent quota by loading up themselves with lots of rubbish French, Italian, Spanish and whatever content.
"Or they could simply remove some of their lesser-watched non-EU material."
The quota plan is not popular in the industry and was immediately criticised by some.
"Cultural quotas are outdated and unnecessary - video-on-demand providers are already investing heavily into European local content," said James Waterworth, Vice President of Europe operations for CCIA, the computer and internet industry association.
Netflix has said it is against quotas or making contributions to film subsidies, instead putting a priority on developing its own content, including in Europe.
Netflix said it already devotes more than a fifth of its catalogue to European content.