Bénédictins (Benedictines)

Monastic order established in 529 by Saint-Benedict.
The Benedictine monks are also referred to as black monks because of the colour of their habit.
The abbaye (abbey) of Cluny was a Benedictine abbey, and the clunisien (Cluniac) Order hence a Benedictine Order.
In the picture (Wikipedia) a medal of the Benedictine Order.

Bénédictins - Wikipedia

Cistercien (Cistercians)

Monastic order founded in and named after Cîteaux.
One of the great abbots of this order was Bernard of Clairvaux.
The Cistercian monks are also referred to as white monks because of the colour of their habit.
The order follows the rules of Saint-Benedict, although strictly speaking they are not a bénédictin (Benedictine) Order.
Sobriety and simplicity are characteristic for Cistercian monastères (monasteries), and most monasteries of this order have a similar lay-out.
The coat of arms comes from Wikipedia.

The coat of arms of the Order - Wikipedia

Clunisien (Cluniac)

Reference to churches and buildings built in commission and under the influence of the Cluniac monastic order.
The Cluniac churches are typified by their richness of ornamentation.

Site Clunisien Saint-Hippolyte (Bonnay)

Grandmontains (Grandmontines)

A monastic order founded in the Limousin around 1076.
The first picture shows the remains of the Grandmontine pirory in La Grange-du-Bois; below that one (from their own website) a plan of one of their monastères (monasteries).

La Grange-du-Bois

Monastère grandmontain - internet

Templiers (Knights Templar)

Members of the (rather military) monastic Order of the Temple. The Order was founded in 1118.
The red cross (Wikipedia) is the coat of arms of the templars.

Templiers - Wikipedia