The StopHS2 Anti high speed rail group says that the 530km HS2 line (and tons of stations) will generate 1.5 million tons of co2, for 18,000 seats an hour 12 hours a day in each direction.

400k seats a day, or 150 million a year, for an average 10kg co2 per seat in construction costs over the first year.

456km London to Paris is is about 100kg co2 each way per seat.

So construction emissions isn’t even a dent in the first year.

Night trains won’t be high-speed TGV services, they will use the regular main lines. Track maintenance needs much less energy than building brand new lines. And yes, the carbon emissions per passenger are higher for high-speed trains compared to the regular ones, mostly because of their construction. Of course all of this works when the electricity produced by renewables or nuclear. If these trains are powered by electricity produced from coal, their carbon emissions are equivalent to using diesel trains.

Don't discount the energy cost of air infrastructure in this comparison though. Airports have a huge amount of tarmac that must be built and maintained, there's the jet fuel production/transportation infrastructure, and of course building the planes themselves. Rail may have the larger overhead, but air has some too.

Alone the amount of tarmac for jet runways is massive. It is also often concrete which has a massive CO2 impact.