Ariane is working on a reusable rocket engine called Prometheus and they created animation of the Themis reusable rocket design.
The Themis project will build a multiple-engine first-stage rocket that launches vertically and lands near the launch site.
The Prometheus engine is a reusable liquid oxygen and methane engine that may cost as little as $1 million to build.
The Prometheus engine will have a thrust of 100 tons each which is similar to the SpaceX Merlin 1D engine. The goal are rockets that are ten times cheaper. The problem is SpaceX is so far ahead with reusable rockets that it is looking increasingly difficult for competitors to ever catch up,
The Themis reusable European rocket could be flying around 2028-2030 but still needs full funding. China is developing the Long March 8-R as a rocket with a reusable first stage. The Long March 8-R should be flying around 2028.
SpaceX is in a position to speed way ahead of everyone else in the business, and competitors will have to go even beyond what SpaceX can do if they want to be important players in the future of space rockets.