I know that the Wikipedia entry still sates that, but I don't think it's correct anymore.

Interestingly enough, Aer Lingus never* codeshared with Air France. They used to codeshare with KLM, for many decades; however, KLM returned to the Dublin route in 2016 after a break of 50 years, which inevitably led to the end of codesharing between AMS and DUB; KLM later returned to the Cork route in 2021 (after COVID spruiked the intended 2020 start) which brought an end to the last EI/KL codeshare route between AMS and ORK.

To the best of my knowledge, EI does not codeshare with any of the other current Skyteam members; they definitely don't codeshare with Delta, which is the only other Skyteam airline serving Dublin, and they don't codeshare with Virgin Atlantic out of either Heathrow or Manchester. It doesn't seem likely that they would codeshare with any of the others; other than flying to the hubs of Air Europa, Czech Airlines and ITA Airways, there simply are no points where Aer Lingus and these other Skyteam airlines could transfer pax one-to-the-other.

United terminated their codeshares with Aer Lingus last October, with barely any advance notice. There is still some limited codesharing between EI and AC, but I am not aware of EI codesharing with any other Star Alliance airline.

Now, of course, Aer Lingus can interline with most/all of the airlines mentioned above; however, they do not codeshare with any of them (other than AC).

As regards oneworld, it finally looks like Aer Lingus is making major strides integrating itself with at least its IAG sister airlines. Aer Lingus takes over the groundhandling functions at DUB for BA, IB and VY soon. They're making changes to Aer Club that align with those being made to the BA Executive Club. We can live in hope, anyway!

*definitely not in the last 20 years anyway