I don't believe that at all, mandatory unions are illegal in Europe yet unions are stronger here. It wouldn't surprise me if making them mandatory actually makes them weaker since workers are so afraid of creating unions that could potentially harm them, while I can always ignore an optional union so they aren't a problem.
I don't think requiring unions is the only way to do it, but the countries that have a high rate of unionization seem to have other incentives in place, such as Sweden and Denmark where unemployment insurance is generally provided through unions in contrast with Norway or France, where this is not the case. The latter countries perhaps consequently have much lower rates of membership, closer to that of the US.
https://www.vox.com/policy-and-politics/2017/4/17/15290674/u...