D-chtoucas de Drinfeld \`a modifications sym\'etriques et identit\'e de changement de base

We give a new proof of the base change fundamental lemma for GL_n for certain Hecke functions by comparing the cohomology of two different moduli space of $D$-shtukas. The original proof, due to Clozel and Labesse, make use of the trace formula and of the unit case due to Kottwitz.