Fiat or crypto?
Fiat - it depends on the exact nature of services you plan to offer, but you'll likely need a Payment Institution license under PSD2 for currency conversion (usually clause 6, Money Remittance). PSD2 is an EU directive so once you get a license in for example France, you can passport the license across the EU and EEA. What will happen with UK due to Brexit is uncertain but everything points to financial services being largely unaffected.
You'll need at least 50,000 EUR but realistically more like 100,000 EUR to get the license, plus costs of running and operating the business.
Crypto - Estonia or Malta are the only EU jurisdictions regulating crypto exchanges right now.
In either case, start by approaching a knowledgeable law firm to guide you through the process.