The OED has examples from 1513 and says ‘chiefly Scottish’. In this case as in many others there is good evidence in Yorkshire from an early date: 1390 ‘going between le Northfeld and le Falghfeld’, Yeadon
1534 to lye open by the space of the hole yere as a fawghe fylde and unsawn, Skewsby
1556 my sone to sawe halfe of the Fawghe, Otley
1586 one gap on the Banck up to the falgh, Farnley Tyas
1642 When yow see tuppe lambs that are well putte forth, buy such, for well happed sheepe are the best for an hard faugh, Elmswell. It was also used as a verb meaning to make fallow: 1578 to burne, faughe, rydd, stubbe, hewe and cut downe all manner of woodes growenge within the said close, Cartworth. Faugh has survived as a minor place-name and Smith has the spelling ‘falgh’ from 1487.