Focus on the region in which you are going to use French the most. If at all possible, make this the accent you will use while you're learning French; it may be difficult to break yourself of a specifically French accent if you are going to be speaking French in Quebec, for instance. Beginning and working with one accent means that you have a step up when interacting with these communities later.
Listen to many samples, audio and visual, of speakers from the region you are focusing on. Try to imitate them very clearly and repeat these listening/speaking exercises often. You cannot learn an accent from written descriptions, so it is important to incorporate audiovisual materials into your learning. You can bolster your accent by listening to news broadcasts and watching films from the region you're studying.
Practice problem letters. French letters or letter combinations that are problems for English speakers include c, ch, e, è and ê vs. é, g, i, j, ll, m, n, o, s, t, u and z, along with diphthongs. The single most difficult letter for foreigners to pronounce, however, is r; moreover, according to research by French speech researchers Philippe Boula de Mareüil and Cécile Woehrling, r is the strongest marker for accent in French. Work with your audio materials, but also tutors or teachers who are familiar with the accent you are focusing on in order to develop the correct pronunciation of r and other problem letters.
Immerse yourself in your target French-speaking community. Before traveling, use My Language Exchange to find a speaker in the region to which you will be traveling to learn what you can work on to improve your accent. In return, you will help her with her English. When you immerse yourself in your target language environment, you will quickly adapt to the accent you hear around you, as well as improving your knowledge of local idioms and slang. Without an extended immersion experience, losing your accent and perfecting a French accent may not be possible.
Visit a vocal coach if, after immersion, you still find yourself with an accent. Vocal coaches experienced in regional French accents can help you work intensively on individual sounds that are problem areas for you. Because this step may be very expensive, it should be considered as the last route toward developing a good French accent.