I know quite a few founders in France and elsewhere.
First off - and I hate doing this - there is the definition game at play here. I sincerely loathe how the start-up community has decided to redefine the word start-up to mean 'business with very large scaling potential' or something to that effect. This removes a lot of the companies that one would normally consider to be start-ups from the equation and also from many discussions.
Of course if your start-up does not have the potential to become a billion dollar company that does not help. So for the moment let's assume those are all still 'in'.
Then, of those companies that you refer to: high tech with international exposure that can sustain a mid-to small company is precisely the sweet spot, SME (small-to-medium sized enterprises), it is the backbone of the economy in many places.
But hardly any of those will be names that people recognize. In Europe we had several of those, and Dailymotion was one of them.
There are quite a few EU based brands that have global recognition: Nokia, Airbus, TomTom, TeamViewer, Skype, HelloFresh, N26, WeTransfer, Revolut, Deliveroo and so on all - maybe except for the first two - at some point in time could claim 'startup' status according to the HN/YC definition of the term.
But for every one of those there are 1000's that do just fine in their local eco-system. The important point is that France is quite underrepresented in that segment, and that is something worrying. More capital isn't necessarily going to solve it, for France to thrive in this sense it would have to change a lot more than just to hold out a bag of money.