Not only the tracks and rails. Trains which travel at these high speeds have to have automated signalling and control systems. If the system goes down they're limited in speed.
The only advantage being that when you hit HS2 tracks, on the way to London, you make HS2 time from then on without having to change train. This is, of course, what France does today. There are only so many LGV. For instance, for me, my LGV runs out at Tours and then it's slower to Poitiers. For anyone running to Bordeaux they run out at Tours too until the new LGV goes in this year.
The longest high speed run they have is from Paris through Lyon and down to Avignon and Marseille.. They also have a new top speed line into Strasbourg now.
You can see the lines with the speeds on this map
It shows that apart from the Red lines the UK is not really that far separated from the rest of Europe and, in fact, our network at it's current high speed is more comprehensive and integrated than many of the other countries, given the distances and sheer size of our network compared to many others.
What that map does show is that there is more need for HS3 first than there is for HS2 right now. But it's to London so we'll see HS2 first.