What sorts of light cavalry were there in high (1300s) medieval western Europe (England and France)? I mean more like non ranged troops. I know that all soldiers likely owned a horse for transport, but were there any lighter types of cavalry that were perhaps used to harass, pursue, take down light infantry, etc? Were poorer knights and men-at-arms (who could maybe only afford a mail coat) perhaps organized into a separate battle to the heavily armoured, well equipped ones?
The most notable use of light cavalry in western Europe during the period you speak of originated in Ireland.
Hobelars were highly mobile cavalry units, and excelled in scouting, reconnaissance and patrols. These units were suited well to the terrain in which military operations had to be conducted in Ireland and other areas with bogs and woods where a superior heavy cavalry would be extremely hampered.
The Jinete of Spain is another notable light cavalry unit from this period. Jinete were Spanish light horseman armed with a javelin, sword and a shield, a troop type developed in the early Middle Ages in response to the massed light cavalry of the Moors. Their primary tactic was to continually harass the enemy until they gave ground or broke their formation.
In France, light cavalry units were almost non-existent during the period. By the 15th century (1445) French light cavalry began appearing, known as Coutilier (also coutillier, coustillier).
Sources and suggested reading:
Warfare in the Medieval World by Carey, Allfree, and Cairns
The Warhorse 1250–1600 by Hyland, Ann
French Medieval Armies 1000-1300 by David Nicolle
In addition to what Courtny found, I discovered that the equivalent English light cav were the Currours. Its tough to find good info about them, but apparently they (like most light cav of the era) were chiefly used for scouting, skirmishing, and (based on the etymology of the word) courier duties. They were also used in the Scottish borderlands.
The Irish countryside supposedly wasn't conducive to heavy cavalry charges, so the Brits needed a more agile and quicker mounted force. Robert Bruce is said to have employed them as well. After a while mounted archers started taking over the English light cav forces though. At the siege of Calis English forces included 5000 mounted archers, and only 600 hobelar.
* - an extinct Irish horse breed. No, it wasn't guys riding around on horse-head sticks with retainers banging together coconuts behind them like in Monty Python's Holy Grail