Abstract : Thanks to their high accuracy, atomic frequency comparisons can be used to perform very stringent tests of the fundamental physical laws. Substantial improvements of these tests are expected, due to recent developments brought by the use of cold atoms and by new advances in the field of optical frequency standards and optical frequency measurements. In this thesis, we first explain how atomic frequency comparisons can be used to test the Equivalence Principle which is the basis of General Relativity. More precisely, these comparisons test the stability of fundamental constants such as the fine structure constant. The remaining of the thesis describes the development of a cold atom fountain using cesium 133 and rubidium 87 atoms, allowing accurate comparisons between the hyperfine frequencies of these two atomic species. The improvement of the accuracy of clocks requires a good understanding of the systematic effects that shift their frequency. In the third part of this thesis, we focus on atom number dependent frequency shifts. The fourth part is a detailed description of the cold atom fountain experiment. The fifth part is devoted to frequency comparison methods between such frequency standards. Finally, we summarize experimental results obtained during this thesis. The accuracies obtained with rubidium and cesium are 2*10^-15 and 1*10^-15 respectively. The best measured frequency stability is 3.5*10^-14*tau^-1/2. The frequency comparisons made during this thesis lead to a test of the stability of the fine structure constant at the level of 7.3*10^-15 per year. This represents a factor 5 improvement over previous tests of the same kind.