So on the GIS - Supported Versions - 10.2.1a - 10.2.1c ArcFM Desktop, Designer, Designer Express, Network Adapter, Fiber Manager, Conduit Manager, License Manager, and Object Reader for Desktop page, at the top, it says: "Please note that while ArcFM requires a specific version of ArcGIS desktop, the version of ArcSDE can differ in the same combinations listed on Esri's Help Documentation, with the exception of ArcFM Replication Server which requires the ArcSDE version to match the ArcGIS version."
If you go to the Client and geodatabase compatibility—ArcGIS Help | ArcGIS for Desktop on Esri's site, they do support running ArcGIS Desktop 10.2.1 against 10.1 SDE, which means ArcFM will support it.
The only caveat is you have to upgrade ArcGIS Desktop to 10.2.1 along with ArcFM.
Thank you David!
It was very helpful.