It may not actually be that urgent, at least for their own use. A non-expendable Falcon 9 launch costs $70m; an Ariane 6 launch costs 80-100m EUR (for a more capable rocket, especially for GTO). Now, SpaceX may be building a lot of profit into that $70m, but from the customer's POV it hardly matters. They're not in drastically different cost realms. The bulk of the cost of most ESA launches would still be the payload, not the launcher.
Also that Falcon 9 cost is up from about $60m a couple of years ago, so you wouldn't necessarily want to bet on it not rising further. And that's list price; in practice SpaceX charges NASA over $100m/launch and "Space Force" over $110m/launch (https://arstechnica.com/space/2025/04/reusable-rockets-are-h...), so, assuming that as another space agency ESA would be charged similar, Ariane may actually be the _budget option_.
Now, for commercial it's a different story, though really Arianespace and its predecessors have never been _hugely_ competitive there; even before SpaceX their market was mostly stuff that couldn't go on Russian rockets.