France & Son Black Label VS. Silver w/numbers  

A chair of mine has both, it...
A chair of mine has both, it looks like one is the company badge and the other has a signature (wanscher?) and serial number on it.
Perhaps it is a design registration number?

I`ve had pieces with both tags before.
The black tag is one of the company logos they used, the silver tag has the France signature along with a serial number and week of manufacture.
I suppose you could date your furniture as being made after the company changed its name from France & Daverkosen which I think was around 63 or 64, but earlier than when it changed to Cado.

Black disc
is the original france and son company logo after it changed from France and daverkosen gold embosed into the frame.
The company dates to late 1948 - 1950 and used the France and Daverkosen up until mid 1950s when it went to France and son and then in 1964 became CADO.
The silver disc is just a serial number as far as I am aware.