As best I can tell, ASFC is only used in France and is synonymous with AGL.
First, it isn't in ICAO's list of abbreviations or the FAA's PCG, but it is in the French AIP in section GEN 2.2:
ASFC / Au dessus de la surface / Above surface
The AIP also lists AGL, but it doesn't explain the difference:
AGL / Au dessus du niveau du sol / Above ground level
Second, the AIP uses both terms in a seemingly interchangeable way. For example, in ENR 1.2 (VFR rules). Compare this from 4.7...
Come over the aerodrome, perpendicular to the runway at 2000 ft AGL,
lights on, then join the circuit for landing
...with this from 4.10:
Fly over the runway at 2000 ft ASFC, perpendicular to the runway
heading with landing lights switched on,
I can't see any reason why there would be any difference in meaning in those two phrases, and the airports in those sections are not particularly near the sea.
Finally, if you consider Wiktionary a valid reference, the definitions for ASFC and AGL are almost the same and they're both stated as the 'opposite' of MSL:
AFSC (Aviation) Désigne une hauteur au-dessus de la surface du sol ou
de l'eau par opposition à une hauteur AMSL, dont la référence est le
niveau moyen de la mer.
AGL (Militaire) Above ground level : « Au-dessus du niveau du sol »,
altitude relative au sol, par opposition à l’altitude absolue, mesurée
par rapport au niveau de la mer.
Although this is a guess, I suspect that ASFC is simply an example of French phraseology that has now been superseded by English but hasn't been updated everywhere. I can't find ASFC used anywhere in a non-French context.