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In order to finish a fleece blanket, you could cut fringe and knot the ends. This creates a look more suited to a throw than a blanket. A simple way to solve this issue is to finish the blanket by sewing a blanket stitch on the edges of its fleece fabric. When you sew a blanket stitch on fleece you can use it as the beginning of a crocheted border or leave it alone for a subtle contrast on the edging of the blanket.
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Start in one corner of the blanket or piece of fleece, moving from right to left along the edge of the fabric. Thread your needle with embroidery thread or floss and tie a knot in the end, then poke it up through the blanket approximately 1/4 inch in from the edge. Pull through until the knot comes up against the back of the fabric.
Insert the needle back through the fleece from top to bottom, positioning it approximately 1/4 inch to the left of your first position.
Pull the needle through the back of the fleece and bring it up and around the edge of the fleece toward the front. Pass the needle through the loop of thread before pulling tightly.
Pull on the thread to tighten the stitch; you should have one vertical stitch and one flat portion of the stitch laying across the edge of the blanket.
Repeat these steps down the entire side of the blanket and around all of the other sides as well, keeping your stitches 1/4 inch apart and 1/4 inch in from the edge of the fabric for a professional, uniform look.