The capacity of the oldest (and probably busiest) European high-speed line (LGV Sud-Est, Paris-Lyon, France) used to be about 12 trains/hour, i.e. a headway of 4 minutes. It's probably around 15 tph nowadays
The minimal headway is dependent on the technology used. France has used variants of the TVM system (TVM 300, TVM 430). Now most new lines are equipped with the new ERTMS/ETCS system. There are several different levels with different performances (in terms of max speed, mostly, AFAIK), though deployment of level 2 has been quite difficult and a lot slower than anticipated (see issues on HSL Zuid and others).
It looks like the minimum headway on ETCS Level 2 is about 2 minutes at 300 km/h. The minimum headway increases slightly as speed goes beyond 300 km/h.
Note that the minimal headway is not the only parameter, as you have many other limitations, including coexistence of trains running at different max speeds, supported signalling, station capacity, merging and splitting traffic (with acceleration and deceleration times), mix of non-stop and stopping traffic (ditto), buffers for delays, etc.
It's probably unreasonable to think that you can actually sustain much more than 15 or maybe 20 trains an hour. Note also that this is usually very concentrated on a few hours each day (with specific patterns around the week-end, holidays, etc.).
If you read french, an interesting and very detailed document on the topic (how to increase the capacity on that line to beyond 12 tph) is available here:
Not extremely recent, but I don't think the overall concepts have changed much since then.
You'll understand that the given capacity constraints have led to the development and large scale deployment of the TGV Duplex trains, in order to maximise the number of passengers transported per train path. Two coupled units can carry well over 1000 passengers.