Context :

Aims : We present a study of the evolved stellar populations in the dwarf spheroidal galaxy Fornax based on wide-area near-infrared observations , aimed at obtaining new independent estimates of its distance and metallicity distribution .
Assessing the reliability of near-infrared methods is most important in view of future space- and ground-based deep near-infrared imaging of resolved stellar systems .

Methods : We have obtained JHK imaging photometry of the stellar populations in Fornax .
The observations cover an 18.5 \times 18.5 arcmin ^ { 2 } central area with a mosaic of SOFI images at the ESO NTT .
Our data sample all the red giant branch ( RGB ) for the whole area .
Deeeper observations reaching the red clump of helium-burning stars have also been obtained for a 4.5 \times 4.5 arcmin ^ { 2 } region .

Results : Near-infrared photometry led to measurements of the distance to Fornax based on the K -band location of the RGB tip and the red clump .
Once corrected for the mean age of the stellar populations in the galaxy , the derived distance modulus is ( m - M ) _ { 0 } = 20.74 \pm 0.11 , corresponding to a distance of 141 Kpc , in good agreement with estimates from optical data .
We have obtained a photometric estimate of the mean metallicity of red giant stars in Fornax from their ( J - K ) and ( V - K ) colors , using several methods .
The effect of the age-metallicity degeneracy on the combined optical-infrared colors is shown to be less important than for optical or infrared colors alone .
By taking age effects into account , we have derived a distribution function of global metallicity [ M/H ] from optical-infrared colors of individual stars .
Our photometric Metallicity Distribution Function covers the range -2.0 < { [ M / H ] } < -0.6 , with a main peak at { [ M / H ] } \simeq - 0.9 and a long tail of metal-poor stars , and less metal-rich stars than derived by recent spectroscopy .
If metallicities from Ca ii triplet lines are correct , this result confirms a scenario of enhanced metal enrichment in the last 1-4 Gyr .

Conclusions :