A henge is a type of earthwork, common in the Neolithic period. It consists of a circular platform surrounded by a ditch, and then a bank, and can be anything from 50 - 400 metres in diameter. Henges are often associated with stone features such as dolmen, circles, standing stones and barrows and are normally contemporary with these, though some henges are older. They are found scattered throughout the UK and Northern France, some henges forming parts of vast ritual landscapes like those found on Orkney or on the Wiltshire Downs.
Henges show a marked change in the organisational structure of the human populations of the Neolithic. The henge predecessor, the Mesolithic causewayed enclosure (a roughly circular platform surrounded by a broken ditch) took some amount of labour to construct, but was nothing compared to the scope of a henge. To support the labourers needed to construct a henge, there would need to be an agricultural system in place, as well as someone to organise the workers. The shift from the mesolithic monuments to the more substantial henges coincides with a change from the hunter-gatherer lifestyle to that of a more sedentary, agricultual way of life, which could have supported the workers needed to build these great monuments.
Many henges would have had wooden structures on top of them when first built, the traces of which can only be found in post holes today. Early woodhenges often come to light on the coast after fierce storms, as these move away the mud and sand deposits that have built up on top of them over time. They date from a time when the English Channel was just a swamp and the North Sea a vast plain covered in grass and woodland. The construction techniques of these early wooden structures can be followed into their stone predecessors, the stone joints at Stonehenge, for example, mimicing the wooden joints of the previous structure. Wood doesn't survive particularly well, and it is only really the stone monuments associated with the henges that survive today. (And even these have suffered! See: Avebury)
As to the uses of the various henges, there are many theories. One is that they were land markers, tying the people to the land they lived in and serving as a type of contract showing their ancestory and rites to the landscape. Another theory is that the henge sites had special ritual significance, many having astronomical alignments with the Winter and Summer Solstice sunrises and sunsets. The sites are often thought to be connected to the Druids, though the Celtic Druids that are often cited as using the sites are later than those who constructed them by some 3000 years. They are places of awe and mystery and well worth a visit. Many are owned by the National Trust or English Heritage, and some of the more famous ones are listed below.
See http://www.henge.org.uk/ for a more complete list of prehistoric sites in the UK.
Henges in the UK
I do not know of any henge sites in France, but am assured by archaeological sources that they do appear there. If anyone knows of any sites, then please /msg me!