According to the Wikipedia article on Adultery
Adultery is no longer a crime in any European country. Among the last Western European countries to repeal their laws were Italy (1969), Malta (1973), Luxembourg (1974), France (1975), Spain (1978), Portugal (1982), Greece (1983), Belgium (1987), Switzerland (1989), and Austria (1997)
The article goes on to list various countries that used to regard it as a crime, and when and how those laws changed. Elsewhere in the article, various non-European countries that regard adultery as a crime are listed.
Similar information is include in an article from The Week "Where is adultery is still illegal?", which says:
The last European nations to decriminalise infidelity were Austria, in 1997, and Romania, in 2006.
The Wikipedia article on Fornication does not list any European country that has current laws against sex between people not married to each other.
It would seem that having an open marriage, or engaging in extramarital sex, is not illegal anywhere in Europe. In some other countries it would be technically illegal but enforcement would be unlikely, while in yet others the risk of enforcement would be significant.