Cool Rocket ! Is the the race for the first methane engine to orbit still on ?

We can send mirage planes, they are being retired. We can't spare any Leclerc though.

I think that's exactly what's going to happen.
They are going to get there on starship with big astronaut crews.
If they want to build their moon base, they going to need a lot of qualified people.
If kg -> moon is not an issue, you will start running out of Astronauts.

If you want the best documentary that isn't really one I would recommend theSpace Brothers anime.
It's really goes in detail into what all the astronaut have to go through before going to space and it's a wonderful story about 2 brothers.

While not a documentary it is the closest I can think of to what you are looking for.

They should change gear TBH. Maintain the rockets for national security reason but expand to other opening fields with this new cheap access to space.
Europe is very good at building satellites and space stations parts.