I think the FAL could work as a DMR. I'd want some mods, though.
-Scope. An ACOG 5x would work for DMR work. You want a lower-power scope with a wide objective.
-Heavier barrel. Nothing super-heavy like DSA's bull barrels, but something like a DSA Medium Contour would work.
-Redesigned handguards. The handguards should be redesigned to allow a sturdy bipod mount (you wouldn't want the bipod on the barrel) and a sling mount (you wouldn't want the sling on the barrel of a DMR either). You'd want the bipod to fold up flush, out of the way. It should be a very sturdy unit, also.
-Stock with cheek piece to help with cheek well.
-Cleaned up trigger. Reliability is more important than a match trigger, though. Must work with hard military primers.
-Flash suppressor, with a threaded barrel for mouting a suppressor.
The barrel needn't be too long. I think DSA's 19" Predator model would be pretty good at the task:
Also acceptable would be the standard medium contour rifle: