The step-descriptions in Brussels and Toulouze are obscure, ambiguous and sometimes seemingly contradictory. This isn't the only valid interpretation: other teachers are likely to do it differently.
Style: All steps involve a smooth rising and falling motion; all steps involve turning the body to some extent ("shoulder-shading", like 15th-century Italian ombreggiare or campeggiare). Forwards steps - simples and doubles - finish with a follow-through (i.e. a single left ends with the right foot poised in front, about to touch the ground). Stand quite close to your partner, and angled somewhat towards them (or away, or both angled left or right: NOT both facing straight ahead).
Each of the steps (one double, one branle, one desmarches, or a pair of simples) takes one bar; usually the music is in 3/2 or 6/4, so I count each bar as 6 beats.