Ariane 6 exists so that European countries can get independent access to space between now and 2030s. The launch cost is almost 2x the cost of Falcon 9. Both platforms can lift 22t to LEO. 6-10 years from now Ariane Next/SALTO will aims replicate Falcon 9 efficiency and the design will be very similar: reusable, RP-1/LOX, Prometheus engine is similar reusable open cycle engine as Merlin with lots of 3D printed parts.
Falcon’s costs are a fiction. SpaceX benefits from massive taxpayer support and uses facilities built by the military and NASA. It’s not a like for like comparison especially give SpaceX keeping its books private and giving no clear public indication of how reusable its rockets really are or their refurb cost. Given Musks history of creative accounting quoting their PR numbers, the ones they pitch congress, as facts…
Ariane 6 was funded by European taxpayers to the tune of €2.815 billion.
>and uses facilities built by the military and NASA.
Ariane is launched from the Guiana Space Centre which is owned and operated by the ESA. Since you haven't familiarised yourself with the topic, ESA is the European Space Agency and is owned by 22 European governments.
In addition, the member states of the ESA will subsidize the rocket for up to €340 million annually in return for an 11% discount on launches.