French dressing will not blend or mix to be creamy
Try adding a bit of egg yolk. The lecithin in that usually helps these things emulsify. Obviously you can't do that if you're young/pregnant/old.

If you don't want to try egg yolk. Put everything in but the oil. Add maybe half the oil and shake, then add a bit more and shake. Do it piece by piece as if you were drizzling into a bowl and mixing by hand with a whisk.