Prussia had stayed neutral the year before and remained outside the Third Coalition, in 1806 they practically engaged the French armies (who were already stationed deep inside Germany) on their own. IIRC, Prussia had about 200.000 troops, France and the CotR c. 300.000.
Stupid move by a weak king.
Jene I give to Napoleon as field commander in any case, while the parallel battle of Auerstädt might go against Davout and for the Prussians who had more than twice the numbers. But it won't be a crushing defeat of the French army.
So many factors are against a Prussian success that I cannot see the events you describe. The Prussian army was nearly obsolete in 1806 without major adaptations to modern warfare since Fred II died. The state administration and logistics were a sorry mess of sometimes feuding feudal holdovers.
You can get a Prussian success in 1806 only if you give Prussia a good reason to modernize earlier. In OTL they needed agood six years to recover and become a Great Power once again, so basically, you might need a PoD with Prussia joining the Second Coalition around 1797 and getting decisively beaten by 1799, opening the way to reforms. Of course, that will create a lot of butterflies.
EDIT: This is Prussia in 1795, pre-Basel. I believe it will lose no other territory to France in an ATL 1799 defeat than the parts of Cleve and Geldern west of the Rhine (to the left of the fortress of Wesel in the map). Perhaps East Prussia to the Batavian Republic, but even that is unlikely in 1799.
EDIT 2: This map has some errors: The area marked as "Kaiserreich Russland" is, in fact Austrian West Galicia. And the dotted border of the HRE is all wrong for any year.