Dear Nicolas,
Yes, you may pick some slang Arabic expressions from Egyptian TV shows, but this is not the way to learn the language. I advise you to start with what is called Modern Spoken Arabic or (MSA). It is called also Modern Fusha and it is used today in media, official correspondence, business, education, etc. After mastering MSA, you can understand Classic Arabic (Fusha) with minimal help of an Arabic/ Arabic dictionary as all Arab people have to do from time to time. MSA can help you also to easily learn a dialect with the help of the vocabulary and structures learnt from MSA. Just to add some expressions of that dialect and you will be able to understand and speak to the native speaker of that dialect fluently. The best dialect to learn is the Egyptian one which is understood all over the Arab world. Next is the Syrian dialect. We are preparing good online courses that can be very helpful to you. They are to be launched in an interactive website in less than 100 days from now. Please see my board for more information.
Best regards,
Youssef