If your leaven floats on top of the water, or even semi-floats, it's ready to bake with. If it sinks completely to the bottom, it has failed the float test.

Does my levain need to float?

The float test is a good general indicator for when a starter or levain has significant fermentation, but I find it is not 100% reliable in testing for when a starter is ready for use. ... Instead of using the float test, I like to look for the signs of strong fermentation and ripeness.

Can I use my starter if it doesn't float?

A starter that will not float is not necessarily a bad sourdough starter. It may just have the ability to float. This could be due to the flour used or the feeding ratio. Instead to tell if it is ready, see how high it rises, how long it takes to rise, signs of bubbles and its smell.