A narrow linewidth operating mode for the Ti:sapphire laser of the CERN ISOLDE Resonance Ionization Laser Ion Source (RILIS) has been developed. This satisfies the laser requirements for the programme of in-source resonance ionization spectroscopy measurements and improves the selectivity for isomer separation using RILIS. A linewidth reduction from typically 10 GHz down to 1 GHz was achieved by the intra-cavity insertion of a second (thick) Fabry-Pérot etalon. Reliable operation during a laser scan was achieved through motorized control of the tilt angle of each etalon. A scanning, stabilization and mode cleaning procedure was developed and implemented in LabVIEW. The narrow linewidth operation was confirmed in a high resolution spectroscopy study of francium isotopes by the Collinear Resonance Ionization Spectroscopy experiment. The resulting laser scans demonstrate the suitability of the laser, in terms of linewidth, spectral purity and stability for high resolution in-source spectroscopy and isomer selective ionization using the RILIS.