'American-influenced' is an English compound formed from 'American' and 'influenced'. 'American' ultimately comes from the personal name 'Amerigo' (Amerigo Vespucci) used to form the place-name 'America'. 'Influenced' originates from Latin, specifically the word 'influere', where 'in-' meant 'into' and 'fluere' meant 'to flow'.

'influere' (Latin) passed into Medieval Latin/Old French as forms such as 'influer' and later into Middle English as 'influence', with the past-participle/adjectival form becoming 'influenced'. 'Amerigo' gave rise to the toponym 'America' in early modern usage, which then formed the adjective 'American'. These elements combined in modern English as the compound 'American-influenced'.

Initially 'influere' meant 'to flow into' (a physical/figurative flow) and was used in contexts including astrological 'influence'; over time it evolved to mean 'to exert effect or power over' and 'shape' — giving the modern sense of 'influenced'. 'American' originally referred to the place-name derived from Amerigo Vespucci and later came to denote things relating to the United States; combined, the compound now means 'shaped by American influence'.