That high speed line should really have more trains, but is that due to the high speed line or SNCF's attitude to competition? There are other cross border HSLs that at least pre-covid saw a lot of trains.
There are actually not that many examples, and almost all in the Northern France-Benelux region, which is extremely densely populated and has historically been extremely well integrated cross-border.
And even there, only the Belgians have really built HSL which primarily serve a cross-border purpose (HSL Brussels - Lille, Liege - Aachen).*
Maybe you got me wrong, though. I am absolutely not against international HSL. I just think that
1. in most cases, you need at least a dual-purpose and domestic demand as well to justify the huge expense building it;
2. the idea that the main aim is to transfer journeys like London - Barcelona or Paris - Berlin from air to rail is wrong. It is never going to happen; and this is not where the major climate benefit will be. Focus on those journeys where a change of mode is more realistic- and these are also the kind of journey where a major impact climate-wise is to be expected because the number of journeys made is so much higher (and a large number of those journeys will be domestic).
*the only other country that has done something comparable is Switzerland - not HSL, but they routinely stump up their own money to improve rail links in neighboring countries (eg München - Lindau, Bourg-en-Bresse - Bellegarde). They have a very pragmatic idea of their own interests; in most countries politics will stand in the way („why pay for someone else?“).