Constraint programs such as those written in highlevel modeling languages (e.g., OPL [15], ZINC [14], or COMET [16]) must be thoroughly verified before being used in applications. Detecting and localizing faults is therefore of great importance to lower the cost of the development of these constraint programs. In a previous work, we introduced a testing framework called CPTEST enabling automated test case generation for detecting non-conformities [13]. In this paper, we enhance this framework to introduce automatic fault localization in constraint programs. Our approach is based on constraint relaxation to identify the constraint that is responsible of a given fault. CPTEST is henceforth able to automatically localize faults in optimized OPL programs. We provide empirical evidence of the effectiveness of this approach on classical benchmark problems, namely Golomb rulers, n-queens, social golfer and car sequencing.