I think most of you focus far to much on the "british" side of the Celts.
I love to play the Celts because I am Briton. And to say a bit like Branoic :
What Civ would I play to beat up the French ?
The Celts covered almost the half of Europe in the 3rd century BC (Time of Alexander The Great), not only the British Isles.
This was a vast civilisation that shared the same culture, religion, and probably a very similar Language.
As a speaker of modern Briton, I can still find some similarities with modern Irish Gaëlic despite more than 2000 years of separate evolution.
The Celts of what is now France, Belgium and northern Italy were called "Gauls". They were conquered by the Romans, but also the roman Empire would never have been so strong if they didn't assimilate the celtic people.
When Brennus threatened Rome around year 330 BC, the Celts already had mastered Iron, and had great Iron sword, the Roman didn't know Iron working. What would have became those mighty Roman legions without the craftskill from the Celts ?
Around 200 BC, the Celts invented the chain mail. Again it was very well re-used by the Romans.
Also the Celts invented the Barrels, and the trousers, this wasn't very much re-used in Rome, but it still remained in the Gallo-Roman civilisation, and survived the fall of Rome.
The Celts of this time were not only fierce undisciplinate warriors, they were also very crafty artisants, and excelled in many field...
Except of course political organization and unity !
But even after the roman ages the Celtic civilisation was still alive even the "romanized" areas.
The root of the French civilisation is by 25% from the Romans (for the language mainly) 25% from the Franks (for the aristocraty, and kingdom rules) and 50% from the Gauls (basically everything else).
As it is said above, the same could be said about the English Civilisation.
And last but not least the celtic culture spread almost everywhere in Europe in the Middle Ages through what is called in French "La matière de Bretagne" (rougly : matter of Britain/Brittany). That is all the literrature about Arthur, Merlin, the knights of the Round Table, Tristan & Iseult, the city of Is, and so on...
And there is no monopoly about this in Great Britain, many novels on the continent were inspired by bards from Brittany.
About Brittany :
I think many people don't know very much about this Celtic realm now possessed by France, so I will tell the basics :
Geography : Brittany is the western peninsula of northern France.
I will use the word "Brythonnic" to talk about the common ancestor of the Welsh, Cornish and modern Britons, to distinguish from the modern Britons.
History : In 476 AD, the Roman Empire fell. The Brythonnics (Christian Celts living in great Britain by then) were left upon themselve to organise their defenses against the barbarian tribes around (the Saxons, the Franks, the Irish and the Scotts were considered barbarians, because they were not christianized). First the Brythonnics settled the Armorican peninsula to control the Britain sea (ancient name for the Channel). This peninsula was left very underpopulated after the collapse of Rome, so the few gallo-romans that lived here welcomed the immigrants. As they almost had the same culture they mixed easlily. Later, the Angle, the Jutes and the Saxons conquered most of Britain, probably mixing with some of the Brythonnics (as said by others). But many of them probably didn't want to live under the saxon's rule and they migrate west, in Wales and Cornwall. Wales and cornwall became overpopulated, so some of them migrate more in little Britain (Brittany).
Until 850 AD Brittany was mostly independant (even from Charlemagne's mighty Empire), but still small, and with no great city. About 850 AD, the king Nominoe of Brittany conquered Rennes (Roazhon) and Nantes (Naoned) which are still now the biggest cities in Brittany. He even conquered other lands (part of Normandy, and Anjou), but those lands didn't last very long in Brittany's hands.
Brittany had it's Golden Age around 14th Century. It was very wealthy but not for long as the endless war between France and England took ground in Brittany.
Independance was over in 1532, but the Britons kept their strong identity until now.
The Briton language, is still alive in the 21st Century, but endagered by French uniformization.
The Celtic culture is still very strong, for example this is a very popular annual Celtic festival, that takes place in Lorient (south-western Britanny) :
http://www.festival-interceltique.com/
http://www.festival-interceltique.com/english_version/accueil_english.php
More about Brittany :
In English :
http://en.wikipedia.org/wiki/Brittany
In French :
http://fr.wikipedia.org/wiki/Bretagne
In Briton :
http://br.wikipedia.org/wiki/Istor_Breizh