I saw on the eurail website that the Paris metro is free with the pass, but what about metros, u-bahns, and s-bahns in Belgium, the Netherlands, and Germany?
The information on the eurail site concerning tranportation bonuses in Paris can be misleading. A eurail pass is valid only on the RER lines (or sections of those lines) that are operated by SNCF, French national rail. It's not valid on the RER A line or ANY Metro line. Those are all operated by RATP, the Paris transportation network.
The eurail site says that the pass is valid on S-bahns in Germany but makes no mention of U-bahns.
Is the RER to Versailles run by SNCF or RATP?
RER Line C is run by SNCF.