Actually there is no European Flight Dispatcher License ...unfortunately!
. That means it depends on whre you want to work.
Exemples: lAustria, Germany, Denmark issue state licenses; it means you need their license
Some countries recognise foreign state licenses or issue airline certificates.
The UK and France do have no license or certification requirement at all; you can work there with any license.
I am French so i can tell you that usally they prefer licenses from the 2 folowing school: ENAC and ESMA (w.ESMA.fr) . Yet if the airline have a lot of flights to the US they might prefer an FAA license. The FAA license has a good reputation.