What is the history of Concorde motto "May Concorde bring people closer" and medal?
That medal is a copy of one that was presented to Queen Elizabeth II by M. Ziegler (S.N.I.A.S) during a state visit by the queen to France in 1972, sometime between 15–19 May. The most likely date would have been 18 May, when she visited a SNIAS helicoper factory and was accompanied by Mr. Ziegler. 

It was presented to commemorate the intention to build the 'Concorde' for commercial supersonic flying and currently sits in the Royal Collection Trust. "M. Ziegler" is Monsieur Henri Ziegler, who passed away in 1998 at age 91. 

"In 1968, he was appointed to run Sud-Aviation, a leading aircraft manufacturer in the south of France, and charged with reorganizing the badly splintered aircraft industry. Sud-Aviation was later absorbed by the larger Societe Nationale Industrielle Aerospatiale, or Snia, which in 1984, as the core of the French aerospace industry, was renamed Aerospatiale S.A."

That is where the "S.N.I.A.S." comes from, "Société nationale industrielle aérospatiale". The Concorde was built by British Aircraft Corporation (BAC) and Sud Aviation. Mr. Ziegler was instrumental to the partnership, and was seen by some, at the time, as a traitor to France for suggesting it. 

I think it is fair to say that this motto was coined by Ziegler for the creation of the medal, likely to express his gratitude for England's role in the partnership, but it is not the official motto of the Concorde.

British Airways' slogan for the Concorde was "Arrive before you leave." I honestly don't remember, nor can I find, a French slogan for the Concorde, but the slogan for Air France is "France is in the air."

It was a lot of fun researching the answer for this.