Do I need to fill out the Eurostar entry card from England to France?

No, because the customs entered France directly from St. Pancler International Railway Station in London. If the documents are complete, it will take about two minutes to pass through the customs. If you want to leave the EU, you must apply for a French visa.

The ticket says: arrive at the station at least one and a half hours in advance, Paris North Station? Paris North Railway Station. The waiting point is on the second floor. There are many people waiting in line, especially the first two trains in the morning. Be sure to arrive early. Go through the customs before getting on the bus, leave the French customs and enter the British customs.

Extended data:

Since the maiden voyage of Eurostar, it has occupied 68% market share of the London-Paris route. As for the route from London to Brussels, it accounts for 63%. Therefore, 3.93 billion tons of carbon dioxide generated by short-distance flights (that is, London to Paris and London to Brussels) were saved, which made an indelible contribution to reducing the greenhouse effect.

Because the operation of the English Channel Tunnel provides many employment opportunities, people and tourists in Britain and France are happy to use this high-speed railway. There is no doubt about the economic benefits brought by this railway.

Baidu Encyclopedia-Eurostar