How can I get new sections of fencing to match the existing fencing?
The original galvanizing of the fence was in a bath of molten tin (hot dip galvanizing).

Since this is not practical for the old fence, there are cold galvanizing compounds.  They are zinc rich paints.  

They will not stop rust that has broken through the original coating.  Rust must be removed, then coat the bare steel. 

The aerosol versions would be very expensive for painting fence, but the compound is available in a brush on version.  Search "Cold Galvanizing Compound for Corrosion Control" and look for liquid brush on versions.