For me, the distances are the most problematic. If we take a look at the map of Europe we can easily see that even the capital cities are relatively close to each other (Paris-Brussels 300 km) and already well covered with the train networks, highways or the airports - thus there is no clear benefit of building the Hyperloop.

Another question would be how to integrate the Hyperloop with the other systems.
Top 4 airports in Europe: London, Paris, Amsterdam, and Frankfurt.
All the major airline companies have some connections there, they are "collecting the passengers" from all over the World.
One or several Hyperloop lines could not make the change in the system.

And the costs, again.
TGV line per kilometer costs between 5 and 20 Million.
Let's assume that Hyperloop cost only double the amount (impossible, but ok).
1000 km track = 40 billions.
It's more than the double budget for NASA (18.4)

GDP of France or Germany is about 2000 - 3000 billion

Imagine the proposal to spend 1% of the total GDP of Germany and France to connect Paris and Berlin.
In other words, to spend the whole military budget of Germany or France to build a train.

Even if possible, probably nobody would be strong enough to build them