France's Prime Minister, Emmanuel Macron, confirmed last Sunday that the country will start welcoming European tourists again on June 15th 2020. This means that there will be no quarantine imposed on those arriving in France from other EU countries. Visitors from non-Schengen countries will be able to enter France from July 1st.
Most European countries, including Germany, Belgium, Croatia and Switzerland will also reopen their borders on June 15th. As for the external EU borders, Brussels will soon create a list of countries in a similar situation to create "safe travel corridors".
All of mainland France is now on a "green zone" virus alert level, which means that Bordeaux is be able to welcome visitors in the safest possible environment.