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I expect you know more about this than me, Terry, but for what its worth here is my twopennorth.
This is obviously a trial run without passengers so should present no problem. The Channel Tunnel and the High Speed 1 line (formerly known as the CTRL) to St.Pancras are basically an extension of the French LGV network so they employ the French TVM-430 in-cab signalling system and work on the same 25kV overhead power supply. The tunnel is constructed to the much bigger dimensions required for the shuttle trains so is no problem, and HS1 is constructed to the UIC continental loading gauge affording the clearances needed for continental trains vis a vis the smaller British loading gauge, so again no problem.
Only the Eurostar trains are allowed to carry passengers through the tunnel at present. They were constructed at great expense with various features not required on surface railways. One of the principal differences is that they capable of being split into two halves in the event of a fire. All the passengers would be evacuated into the half that is not on fire, the train then split and driven out of the tunnel.
This feature has never been used. All three fires in the tunnel have been on freight shuttles. The argument therefore is that this feature is unnecessarily prescriptive and can be relaxed without impinging on safety. This would enable French TGV and German ICE trains to use the tunnel without major redesign. The Intergovernmental Commission responsible for tunnel safety is giving this due consideration.
Both SNCF and DB are very interested in running international trains to London. I believe there is an EU policy on open access about to come into force which will have a bearing on this. Also, the UK part of Eurostar is up for sale and is expected to be taken over by Deutsche Bahn, who already operate almost all the freight in the UK after purchasing EWS, and also own Chiltern Railways.
The main sticking point for operating trains to other destinations on the continent apart from Paris and Brussels is that the UK is not party to the Schengen agreement. All international trains on the continent within the Schengen area travel across borders without any border controls. The UK requires that all passengers at both ends pass through immigration controls. This requires separate platforms sealed off from the local platforms and no intermingling of international and local passengers at any stops enroute. Providing these facilities at a multiplicity of destinations such as Amsterdam, Cologne, etc, would be very expensive and quite possibly impractical where the space for constructing dedicated platforms does not exist.