I think we can probably rule out French uniforms. Joubert's force was formed from the Mpala garrison raised by the Belgian Émile Storms, who served King Leopold's International African Association. When Storms was recalled in 1885, he handed the garrison over to the White Fathers.
The earliest mercenary forces of the International African Association had no uniforms, the askari wore whatever was traditional to their culture (e.g. the Zanzibaris wore long white gowns with fezzes or turbans). But in the early 1880s they started to receive uniforms, similar to those of the later Force Publique. That is to say blue jerseys and breeches.
I have found no description of the Mpala garrison's appearance, so cannot say if they were ever issued uniforms. But if they were, they probably would have looked like Belgian askari, though probably pretty ragged and with some variation. Once under the White Fathers they probably would not have received replacement garments from the Belgians, so their appearance could have varied wildly, unless the White Fathers came up with a uniform of their own. And I have seen no reference to this happening.
So not much to go on, but I hope that helps a bit.