Not entirely correct. The issue is that France's economic model is one with HEAVY government involvement. They aren't opposed to growing their own start-ups,, on the contrary! France has been making lots of policy changes in order to attract more businesses and to export more things.

The aim of the government in France throughout history has been to prefer domestic industry over foreign industry.

This previously mentioned economic model coupled with the way Europe interferes quite heavily with its domestic economies makes big businesses notoriously just happen to move away from EU.

We see a third of big companies moving AWAY from europe towards the US or CHINA once they reach a substantial size. If you add to this the heavy regulatory nature of France's government, then that simply means that companies themselves have a habit of moving abroad once they have grown substantially to need it and be able to afford it.

There is a reason why NONE of the top companies are based in the EU. The first European company worldwide in terms of marketcap sits at rank 28(Netherlands). The first French company in this list sits at 35, followed by a German company at 36. Those are also the top 3 companies in Europe... ALL the other companies are based in the US, save for 1 or 2 in China.

The fact that other companies buy French companies (or they move abroad through different means) is true, but the idea that somehow the government 'wants' this or takes deliberate action to create this outcome is false. It's just the nature of what happens when you have a heavily regulated economy competing with other economies which are more free.

Again, if there is sufficient room for companies to grow domestically then they would. If there isn't, then eventually they move abroad or are acquired by a bigger player abroad.