France in 1869 was already a constitutional monarchy, or close to it, and it was the elected politicians who pushed France into the war. So no, the Franco-Prussian War is not averted.
Where this timeline gets interesting is that the early death of the younger Louis-Napoleon gets butterflied away. There is no need to send an ex-Emperor to a colonial war. He might get himself killed during the Franco-Prussian War, however.
What I had in mind as a PoD involved avoiding the Franco-Prussian War altogether, having France actually win it would likely mean getting Austria-Hungary involved. It might also mean France taking not only Luxembourg but also Wallonia and/or the Saar, depending on who else enters the conflictPerhaps POD would be before 1869? Or then France winning the war so monarchy is not ousted.