Shabbat Shira is always a beautiful week in synagogue. The bakashot are spectacular and the hazan will fill the room with some of the most beautiful melodies to sing. It has become a staple in synagogue's around the world that Shabbat Parashat Beshalah is known as a day of song and joy.
Moroccan Jews have the custom to add special lines preceding the recital of Az Yashir Moshe specifically on Shabbat Beshalah. They are sung in the same traditional tune as Az Yashir Moshe.
The song Ashira Keshirat Moshe can be found here: (Az Yashir Moshe is below)
French Moroccan Jews were accustomed to sing different melodies for Az Yashir Moshe for every week with different maqamim. (For example see HERE in maqam zarka). They would only sing the traditional tune for Shabbat Beshalah.
Spanish Moroccan Jews almost always sang the traditional tune and only on the Hagim did the paytanim change the tune. Whichever group you belong to, knowing the traditional tune for Az Yashir Moshe is a must. Here it is: