Don’t want to belittle the achievement but they launched it as in „had it launched by the commercial launch provider SpaceX“, not on a self-developed rocket as it sounds like on the first read.
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An organization that can produce Ariane 6 should be able to produce a Falcon 9 clone with similar effort. The real problem is overcoming the of the old, slow, expensive way of doing things.
If anything Europe has the opposite problem: the launch startups are all far too small to do anything on a Falcon 9 scale. SpaceX did't get to Falcon 9 early either. Sure, Arianespace probably could build a Falcon 9 clone, but it's not something they'd want to self fund, and there's quite a few ESA members that don't want to see most of their budget contributions go to funding the development of a foreign launch monopolist...