[Ibrîniðilpathânezel]

From Letter 131:

The Hobbits are, of course, really meant to be a branch of the specifically human race (not Elves or Dwarves) -- hence the two kinds can dwell together (as at Bree), and are called just the Big Folk and Little Folk. They are entirely without non-human powers, but are represented as being more in touch with 'nature' (the soil and other living things, plants and animals), and abnormally, for humans, free from ambition or greed of wealth. They are made small (little more than half human stature, but dwindling as the years pass) partly to exhibit the pettiness of man, plain unimaginative parochial man -- though not with either the smallness or the savageness of Swift, and mainly to show up, in creatures of very small physical power, the amazing and unexpected heroism of ordinary men 'at a pinch.'

In that same letter, Tolkien also says:

Their origin is unknown (even to themselves) for they escaped the notice of the great, or the civilised peoples with records, and kept none themselves, save vague oral traditions, until they had migrated from the borders of Mirkwood, fleeing from the Shadow, and wandered westward, coming into contact with the last remnants of the Kingdom of Arnor.

That the Hobbits were granted the Shire as a fiefdom of the North Kingdom seems to indicate that both the Men and the Hobbits recognized that they were somehow part of the same human race. As such, they would both be Children of Eru, even though Hobbits did not come to the notice of the other races early on -- which was possibly part of Eru's design for them.