It developed from the late 17th century manteau which had a full back and front pleated to fit the body and a train. The pleats were held in place by a belt, sometimes also by hidden tacking.
French fashion forgot about the manteau after the death of Louis XIV and the subsequent turn towards looser gowns - most notably the contouche - but in England it survived and was worn as often as the contouche.
In the English version, the pleats were stitched down firmly, the train folded back up to the waist, so that it didn't brush the ground. The gathered-back sides of the skirt often affected a bowtie shape when seen from the back. Some (probably everyday) 1730s gowns didn't have a train anymore; later on, the train vanished altogether.
In the second half of the century, the Anglaise was re-imported into France (hence the name) and welcomed as more "simple" than the prevailing French styles although the construction really isn't simpler.The anglaise only lacked the ruffle-and-bow decoration which had only been a 1750s/60s fad, anyway. In any case, simplicity suited the new trend towards the end of the century. The anglaise was first worn with a short train over small or pocket hoops, just like the francaise. Later - around the 1780s - it lost its train altogether and was only supported by bum and/or hip pads.
Jackets also have the anglaise/française distinction, which invaribly comes down to tacked down vs. loose pleats in back.
Examples of manteaux:
17th century manteau
1720s English mantua
1770s English mantuas
1780s French manteau