The current International System of units (SI) is built on a choice of seven well-defined base units : the meter, the kilogram, the second, the kelvin, the ampere, the mole and the candela. The definition of some of these units is based on macroscopic object or macroscopic properties of matter, which is unsatisfactory. A revision of the SI is thus expected at the next meeting of the Conference Générale des Poids et Mesures (CPGM) in 2015. For this occasion, a new definition of the kelvin will be implemented by fixing the value of the Boltzmann constant. The current recommended value of this constant is however mostly based on results obtained using a single method, namely the acoustic gas thermometry. The experiment being developed at the Laboratoire de Physique des Lasers aims to provide a competitive measurement of the Boltzmann constant using an alternative method, the Doppler Broadening Thermometry (DBT), based on high resolution laser spectroscopy. The developments, improvements and studies realized during my thesis will be described. Looking at the obtained results and envisaged prospects, it will be concluded that a competitive measurement of the Boltzmann constant by the DBT and before 2015 is well within reach.