In global navigation satellite system (GNSS) data processing, precise point positioning (PPP) with ambiguity resolution (PPP-AR) is a versatile technique that aims to achieve centimetre-level accuracy by resolving integer ambiguities in carrier phase observations. However, the inherent errors and biases in the satellite signals can degrade the performance of PPP-AR solutions. To mitigate such errors, this research proposed to argument PPP-AR using third-generation BeiDou Navigation Satellite System (BDS-3) multi-frequency observations and the observable-specific signal biases (OSBs) generated at the Centre National D'Etudes Spatiales (CNES). To test the proposed technique, both BDS-3 and Galileo observations from the multi-GNSS experiment network were used, in consideration that the latter also transmits multi-frequency signals. Before demonstrating the impact of CNES bias products on PPP-AR, the quality of BDS-3 and Galileo signals was assessed. The results indicated that the modernised frequencies had the best signal strength. The mean standard deviations for the estimated OSB for different receivers were close to each other in both constellations. Besides, the positioning results in different processing schemes unveiled a comparable positioning accuracy, and slightly better in the quad-PPP strategy using the Galileo constellation in both static and kinematic modes. Galileo also attained better ambiguity fixing rates and convergence time than BDS-3. Finally, there were slight differences in the magnitude of the estimated phase residuals for distinct frequency signals between BDS-3 and Galileo, including the interoperable and compatible signals.