These people appear to have been mixed in ancestry.

According to C. Loring Brace:

This placement suggests that there may have been a Sub-Saharan African element in the make-up of the Natufians (the putative ancestors of the subsequent Neolithic

In that run, the Natufian of Israel ties to the French Mesolithic and then to the Afalou/Taforalt sample from North Africa

The interbreeding of the incoming Neolithic people with the in situ foragers diluted the Sub-Saharan traces that may have come with the Neolithic spread so that no discoverable element of that remained
From another source:

Analysis of morphological variability in the Near East and Europe (here and in Pinhasi 2003) suggests that the Epipalaeolithic populations from the Natufian Levant were noticeably different to the Mesolithic populations described from the Danube Gorge, the western Mediterranean, and central Europe. No close similarities were observed between Early Neolithic and Mesolithic European groups in any of the regions studied, with the possible exception of Mediterranean Europe. However, neither were clear affinities observed between Epipalaeolithic Near Eastern groups and any other Neolithic or Mesolithic groups.
Finally, Carleton Coon on the Natufians:

Compared with the continent of Africa, from the prehistoric standpoint, Asia is little known. So far, excavations have revealed implements of Mesolithic technique in Kurdistan and in Palestine,8 but only from the latter have Mesolithic skeletons been recovered. Here an Aurignacian culture lasted during the entire Late Pleistocene, and directly preceded the Mesolithic. Since Miss Garrod feels that this region was one of the main areas of differentiation of the Aurignacian cultural technique, it is very unfortunate that not a single Aurignacian skull has been published. Therefore, the very important question of the Late Pleistocene relationships of this key area must remain unsettled.

For the following period, however, at least two hundred skeletons have been exhumed from two different Mesolithic levels and from five or more sites. So far, only two of these skeletons have been published, one from each level. Great doubt is current at the moment concerning the exact nature of the physical types of this people, and we must await detailed publications in the near future before this matter may be settled.9

These Palestinians, who have been given the name Natufians, apparently differed in physical type from period to period. One of the two skeletons which has been published is that of an adult female from the earliest level at a site called Erg el Ahmar.10

The skull of this woman is large, robust, and thick-walled; it is purely dolichocephalic, and has an elevated cranial vault in which the height almost equals the breadth. The forehead, as with females of many races, is broad, straight, and rounded. The face, likewise, is broad, and of medium height; the nasal root, somewhat depressed, is hidden under browridges massive for a female, while the nasal bones project far forward, to form an accentuated profile.

The low, broad orbits of this specimen assume the rectangular form characteristic among most of the Upper Palaeolithic skulls from Europe and North Africa, while the orbital index is correspondingly low. The nose is high, narrow, and metrically leptorrhine; the nasal spine prominent, and the lower border of the piriform opening strongly crested. The mandible, of medium robusticity, possesses a prominent chin. The rugged beauty of this Natufian woman was, however, somewhat diminished by an abnormality of dental occlusion, for her lower incisors overlap the upper ones.

Morphologically, this skull is perfectly European and belongs Without question to the general Upper Palaeolithic type. It would also fit metri.. cally into the female range for this group. It would, however, fit equally well into the North African series of Afalou bou Rummel, except that it is somewhat narrower nosed than the females of that group as known at present.11 In the absence of data on Palestinian Aurignacian crania, one may suppose that the Aurignacian Upper Palaeolithic Neanderthal-sapiens hybrid developed in this neighborhood from Skhul-like beginnings, and that this Erg el Ahmar female is a survival of it.

The skulls from the later Natufian period, while exceedingly numerous, remain dubiously classified because of several conflicting ideas about them which have been published. Sir Arthur Keith12 in a preliminary report on the remains from Shuqbah and Kebara, states that the later Natuflans were short people, the males having a mean stature of 160 cm. and the females of 152 cm. The tallest male in the group was only 165 cm. in height. The hands and feet of these later Natufians were remarkably small, and their long bones were in no sense massive.

The skulls which Keith describes are of a peculiarly Mediterranean type, with a cephalic index ranging from 72 to 78, thus rivalling the subdolichocephalic head form of short statured Mediterraneans living today. The brain cases are of medium size, and the faces absolutely small. The lower jaws are also small and weakly developed, with little chin prominence and a prevalence of alveolar prognathism. The wide, low-vaulted nose, in combination with prognathism, gives a somewhat negroid cast to the face. The browridges are smooth, and the whole system of muscularity in the male but slightly developed. These late Natufians represent a basically Mediterranean type with minor negroid affinities.13 There was, apparently, a change of race during the Natufian. These small Mediterraneans must have brought their microliths from some point farther south or east, impelled by changes of climate.