Abstract: In this study, new approach is proposed based on wavelets analysis for investigating the relationship between the return of the stock and its systematic risk in the Capital Asset Pricing Model (CAPM) at different time scales for French’s stock market. The proposed procedure is acted on a sample composed of twenty-six stocks actively traded over 2002-2005. It has proved that the relationship between the return of a stock and its beta is more robust at short and long scales. This evidence shows that the French’s stock market is more efficient at shorten and longer period. Therefore, the predictions of the CAPM are more relevant at short and long-term horizon in a multi scale framework as compared to other time horizons.