We have performed photometric CCD observations of the giant and horizontal branches of the globular cluster1, and of the giant branch of cluster3, in the Fornax dwarf spheroidal galaxy. The observations were performed in the V and I standard broad-band filters as well as through two narrow-band filters especially designed to distinguish between carbon and M type stars. The AGB is richly populated with carbon-rich stars, and all of them are considerably below the theoretical lower luminosity limit for such stars. If the Fornax clusters are interpreted as resembling an earlier epoch of the Galactic globular clusters, the low luminosities of the carbon stars therefore point to a larger role of the low-mass stars in the chemical enrichment of our Galaxy. The giant branches of the Fornax clusters are much broader than canonical giant branches in Galactic globulars, and the AGB is more well populated. We suggest that the morphology and stellar population of the giant branches indicate that the dwarf galaxies are =~3Gyr younger than the Galactic halo, which in turn seems to be =~3Gyr younger than the Galactic globular clusters. For a description of the N2-N3 photometric system, see e.g. <GCPD/39>