Multifractal techniques are applied to the study of rainfall daily time series over France simulated by the climate model CNRM-CM3 of Meteo France in a coupled climate scenario A2 over the period 1860-2100. We quantify the scaling variability of the simulated rainfall with the help of a few relevant multifractal exponents characterizing the intermittency and multifractality of the field. These multifractal exponents are determined by the Double Trace Moment (DTM), which shows a scaling range from one day to about 16 days. The opposite trends found in the evolution of the intermittency and multifractality exponents have contradictory effects on the evolution of the extremes. However, a refined analysis shows that due to the dominant effect of intermittency increase, we may expect an effective increase of rainfall extremes for the next hundred years.