Topping up Monzo card from non-GBP currency will most likely be quite expensive. You can make bank transfer to Monzo or top up with card in EUR, but applied exchange rate will be of your bank, not Monzo. While I don’t know what currency exchange rate and fees your bank applies, but that most likely can’t be a very good rate. Then, as you spend money with Monzo you’ll be exposing yourself to second-time currency exchange. Even if you would top up in EUR and spend in GBP, you are still getting that less favourable exchange rate from your bank.
There are other solutions that might be suitable for you. Monzo plans to expand to Europe, but that’s not happening soon. Other cards, like Revolut, have other currencies including EUR, so you can top up in EUR, then spend EUR. Revolut’s exchange rates are on par or tiny bit worse in comparison to Monzo. I would recommend more research if that’s good option for you, but that seems better than exchanging currency twice (EUR -> GBP -> EUR).