In neighboring countries there is usually no additional reservation requirement for trains during these corona times. In the Netherlands you only need to make a reservation if you want to take the bicycle with you. In France, the TGV or high-speed train must be reserved in advance, but it used to be that way. This does not apply to the other trains. An idea to introduce that reservation there, too, was thrown out last year after protests from train travelers. A reservation is also mandatory for all other high-speed trains such as the Eurostar and Thalys.
Almost all rail companies in neighboring countries recommend avoiding rush hours and opting for quieter moments, but that is not an obligation. The same corona measures also apply almost everywhere, such as wearing respirators in stations, on platforms and in trains, keeping as much distance as possible and the like. In Italy, the government does require a statement from the traveler that they do not feel sick and have no symptoms.