Pouring Curbing On Existing Concrete
It sounds to me like you are essentially asking how to make a 'raised curb'

Building a form, mixing, pouring and floating all this concrete is pretty labor intensive. Before you start, you may want to consider an edging made out of paving stones would be far easier to contour and a much faster install. 

I'm not an expert, but live in a city where people are in charge of their own side walks and thus there's always a lot of refinishing activity going on. I have never seen anyone overlap the uppermost surface of concrete unless they are doing pouring over an entire slab with 4" of fresh concrete.  Thus, much like the raised curbs you see around you, it's best if there is either:


a slight gap between the existing concrete




or


An an edged in joint exactly where the new and old concrete mate




TLDR;

Contorting a form above your existing concrete will likely to be harder than seating it into your trench and using the edge of your existing concrete as a brace.  If you use something like (15/32") treated plywood to make your form, you can cut it flush with your existing concrete once your new form has dried and it will act as your expansion joint.