Aircraft were issued to Jasta as they became available, and it was unusual for a Jasta to convert wholesale from one aircraft type to another. As 1918 began, it would be quite usual for a Jasta to be fielding brand new Fokker D-VII alongside Albatros D-V and D-III alongside Pfalz D-III alongside Fokker Dr-1.
The ideal, of course, would be for every pilot to be flying the same type, if only to ease logistics. But having a flyable plane in the air was more important than keeping consistency across a squadron. By the very nature of their construction, WW1-era planes wore out pretty fast, even if they survived combat, so there was quite a lot of "churn" in squadron aircraft types.
In practice, senior pilots could choose the type they flew, but as far as I am aware it was not official doctrine.
Things were much more rigid in the RFC. I don't know much about the culture of the French flying services.