Do Brazil and France have a common border?

Yes, Brazil and France do have a common border. It is the Oiapoque/Oyapok river that separates the Northeastern tip of Brazil from French Guyana.

OK, you can say that French Guyana is a French colony and would not qualify as being France itself, however:

Unlike other French colonies, French Guyana is technically a French Overseas Territory (Territoire D'Outre Mèr) and therefore it is technically part of France itself. And the Brazilian state of Amapá is part of Brazil. Which means that the Oiapoque/Oyapok river is actually an international boundary between the two countries.

There is a modern bridge that crosses the Oiapoque or Oyapok river from the Brazilian side to St. Georges de L'Oyapok on the French side.

This means that it is actually possible to easily walk, swim or take a small boat ride from Brazil to France in less than an hour, or take a bus or drive from one country to the other in just a few minutes. That beats the close to 11-hour flight from São Paulo to Paris, if you only consider traveling between Brazil and France and not between better-known destinations in either country...