Euronext is registered in Amsterdam and has its corporate headquarters in Paris so there will be no issue at all with any offices it has in London other than possibly shutting them down.
This would include all properties including data centers and I would find it strange that a company of this size would not already be working on the needed moves in case of a hard brexit. However the question would be is there any need to move the datacenter as the company is a European stock exchange and not a Euro one so I would guess that it would not matter.
A much bigger issue that was not asked would be what would happen to all of the English companies that are listed on it and if they would have to be removed which could possibly cause not only those companies major issues but the entire Euronext market as there is now a precedent of entire countries being removed. Because of this I don't think there will be any impact to them.
Euronext N.V. (European New Exchange Technology) is a European stock exchange with registered office in Amsterdam and corporate headquarters at La Défense in Greater Paris which operates markets in Amsterdam, Brussels, London, Lisbon, Dublin, Oslo and Paris. With around 1,500 listed companies worth €4.1 trillion in market capitalisation as of end July 2019, Euronext is the largest stock exchange in continental Europe. In addition to cash and derivatives markets, Euronext provides listing market data, market solutions[clarification needed], custody and settlement services. Its total product offering includes equities, exchange-traded funds, warrants and certificates, bonds, derivatives, commodities and indices as well as a foreign exchange trading platform.