In flat, free, Euclidean space, the shortest path and the zero acceleration path are the same path, which is a straight line. However, in general relativity, is the zero acceleration path also the shortest path between two points? I am assuming that free fall is zero acceleration.
In general relativity, you're dealing with a 4D spacetime, so the "points" in spacetime are events, and the measures that you can make coordinate-independent statements about are intervals instead of distances.
The rule that applies is that the world line with the longest possible proper time between two events is a world line that involves zero proper acceleration. Such a world line is called a "time-like geodesic".
There's a similar concept for space-like curves. A "space-like geodesic" is a curve with a stationary proper length between two events with a space-like separation. A space-like geodesic is locally straight.
For more information, see the Wikipedia article section "Geodesics as curves of stationary interval"
And yes, free fall means zero proper acceleration.