A good discussion in general, but the etymological part is out of date. You say:
Where the French word comes from is uncertain, but a few roots are commonly proffered:
• the Latin radix, meaning root
• the Latin generatio, from which it is a clipping
• the Arabic faras, meaning horse
All of these are plausible, but there is no strong evidence for any one of them.
The last two sound completely implausible to me (credential: MPhil in historical linguistics), and I presume the first has been rejected for good and sufficient reasons though I don’t know enough about the development of Late Latin/Romance to know why; the OED (Third Edition, June 2008) goes with my off-the-cuff guess once I saw your mention of haras:
Apparently originally aphetic < haras n., probably subsequently reanalysed as showing a spec. sense of race n.6 (compare race n.6 2b).