A homemade brioche dough can be frozen but the main concern here is that the dough once thawed and proofed usually does not perform well as the freshly made dough. Therefore its not recommendable.
Just plastic wrap is enough. There are two methods for Freezer Doughs: First, you can mix, knead, and shape the dough into a disk. Instead of letting dough rise, wrap the disk airtight and freeze. Thaw dough in the refrigerator, in the microwave oven, or at room temperature; then shape, let rise, and bake. Or you can freeze the dough after shaping. Thaw it in the refrigerator or at room temperature, let it rise, and then bake.