The SPE DR1-Foundation data processing is described in detail in the Euclid Quick Data Release (Q1). Characteristics and limitations of the spectroscopic measurements. The quality of the SIR spectra has greatly improved in DR1 with respect to Q1, and the SPE PF has also been updated. The DR1 version is described in Euclid Data Release 1 (DR1). Performance of the redshift measurement and spectroscopic analysis together with extensive tests.