'form-based' originates as an English compound of 'form' and 'based'; 'form' originates from Latin 'forma', where 'forma' meant 'shape' or 'form', and 'based' comes from the past-participle use of 'base', ultimately from Old French/Latin roots (see below).

'form-based' developed in modern English by combining the noun 'form' with the adjectival past participle 'based' (from 'base'). The word 'form' came into English from Latin 'forma' via Old French and late Latin usage, and 'base' entered English via Old French (e.g. 'baser') ultimately from Latin/Greek 'basis'. Over time the past-participle 'based' was used to form compounds meaning 'having X as a basis', producing constructions like 'form-based'.

Initially 'form' meant 'shape, appearance' and 'base' meant 'foundation'; combined in modern usage they specifically mean 'having something founded on or organized by form(s)' rather than literal physical shape.