We know that the Furneaux came from a place called Fourneaux, in France, around the time of William the Conqueror. However, as there are many different places called Fourenaux in France, is it not clear exactly which place is being referred to in the various manuscripts. I have plotted all the names of the various Fourneaux in France, on the map below. Please note the cluster near Normandy (NW corner). The sources for each of these locations, a summary of where they were found, and brief comments on each are provided below. In order to consider each of these places, it is important to remember that the Furneaux were Normans, and therefore likely to be from Normandy. Falaise

Falaise is on the map. While not a known location of the Furneaux prior to 1066, it was the seat of William the Conqueror, so is important to consider in relation to the other sites. If you zoom in on the cluster of locations in the top left hand corner of the map above you will see they occur close to Falaise. Fourneaux, Manche, France: 

This site is proposed by multiple authors, and contemporary academics. Alternative names in documents appear to be Fourneaux-sur-Vire (1828), Fornels (1159),   Furnellis (~1180),  Fornaus (1253),  Fourneaulx (1494),  les Fourniaulx (1509). See the variations on the  family name for an interesting comparison. Apparently Dr Katherine Keats-Rohan suggested this was the preferable site, although agreeing there is little evidence to confirm this over Fourneaux-le-Val. Fourneaux-le-Val, France

This location has also been proposed by multiple authors. Alternative or historic names appear to have been Fourneaux, Calvados, and Furneaux-sur-Baise. It is probably a good thing that the latter name didn’t stick. These two first sites have higher credibility, at least in my mind, than others listed below. Primarily this is because they are all situated in Normandy, and the Furneaux history in the UK starts with the Norman invasion after all. These sites have also been nominated in various texts. Other locations called Fourneaux The other locations called Founeaux in the map above, are all outside of Normandy, so seem unlikely to be where the UK branch of the family commenced.

• Fourneaux, Chaingy, France
• Fourneaux, Saint-Médard-la-Rochette, France
• Fourneaux, Dunières, France
• Fourneaux, Saint-Jean-de-Maurienne

Conclusion It seems that the most likely locations are either Fourneaux, Manche or Furneaux-le-val. A summary of each location, comments and likelihood is provided below, as well as links to the specific location.

Summary of Places Associated with Furneaux in France

Location	Source (Authority)	Comments	Likelihood of Originn of
Fourneaux, Manche, France	Oxford Dictionary of Family Names in Britain and Ireland	Apparently only Fourneaux mentioned on it's own without qualifiers in Normandy. Proposed by many authors once alternative names taken into account	Possible. If same as Fourneaux near St Lo and Fourneaux near Contances then mentioned in most references.
Fourneaux-sur-Vire, near St Lo	Proceedings of Battle Conference Patronymica Britannica	Search engine gives same location as Fourneaux, Manche. Apparently, this was only the name of the town in the early 1800s and reverted to Fourneaux. It was a manorial fief.	Possible Site apparently favoured by Dr Keats-Rohan, but there is little evidence to favour this over other sites in Normandy.
Fourneaux, near Coutances	Miscellanea Genealogica et Heraldica The Battle Abbey Roll	Unclear where this place is. The nearest was Fourneaux, Manche (33km away)	Possible
Fourneaux-le-Val, France	Proceedings of Battle Conference	Closest to Falaise, seat of William the Conqueror Proposed by many authors once alternative names taken into account	Possible Alternative site suggested by Dr Bearman
Fourneau-sur-Baise, near Falaise	Patronymica Britannica	Could not find on current day maps. Apparently Fourneaux-sur-Baise was a proposed name for Furneaux-le-Val, but the name didn't stick. This is probably a good thing as the modern translation is unfortunate.	Possible
Fourneaux, Calvados	Oxford Dictionary of Family Names in Britain and Ireland	Seems to be the same location as Fourneaux-de-Val. Apparently, previous name for Fourneaux-le-Val	Possible
Le Vieux Fourneaux, Vaux-sur-Seulles, France		This only appears via search engines, not a town or commune. Not nominated by any authors. Near Bayeux	Unlikely
Fourneaux, Chaingy, France		Found via search engine, not referenced in texts. Not in Normandy.	Unlikely
Fourneaux, Saint-Médard-la-Rochette, France		Found via search engine, not referenced in texts. Not in Normandy.	Unlikely
Fourneaux, Dunières, France		Found via search engine, not referenced in texts. Not in Normandy.	Unlikely
Fourneaux, Saint-Jean-de-Maurienne		Found via search engine, not referenced in texts. Not in Normandy.	Unlikely