You're framing this as if it's the EU's job. It isn't.
The only way the EU could compete if it would become a federal state, similar to the US. Right now the EU, despite being a single market in many respects is far from being a true digital single market.
Individual states are actively fighting against this because they would have give up bits of their sovereignty (controlling tax levels, such as VAT, commercial legislation, etc.).
You can't both have your cake (a huge single market able to funnel huge amounts of money into your desired investments) and eat it (keep total control of your country's finances).
Every EU country pushes back when there are attempts for more integration. More than that, there's a rising anti-EU current in most EU countries, due to various population movement issues.
Then what is EU Horizon 2020 for?
https://ec.europa.eu/programmes/horizon2020/what-horizon-202...
But the EU budget is much, much smaller than the US federal budget:
EU: $150 billion for 2014
US: $3000 billion for 2014
And the barriers between national markets in the EU are much steeper than the ones between state markets in the US.
- Vaguely defined, so they open a lot of room for lobbying and corruption
- It is hard to align them to a startup agenda and the administrative overhead is often prohibitive
I wish it was more like a venture fund, but one that doesn't take equity.
Just my two cents.
I think this is less about regulations and more about language. Most people in the EU simply don't speak english so you would have to have your marketing and sales in 20 languages which is simply not doable. A french startup just can't cold call a romanian company because they can not communicate. Yes, it gets better with each new generation but it will be decades before this is "solved".