We are running with a 10.0 database and desktop.
While mixed ArcFM versions is technically not supported (10.0 Desktop and 10.2 Server), since you're not editing, this should probably work.
I'm guessing that you're pointing your 10.2 ArcFM Server at your 10.0.x License Manager? If so, that's likely the problem. 10.1.1 and higher (so, 10.2 and 10.2.1 at the time of writing) require new updated license xml files, and if you're pointing ArcFM Server 10.2 at an old license manager, that won't work. You'll need to split off your ArcFM Server license and load that up in an updated license manager.