The European Centre for Medium-Range Weather Forecasts is currently based in Reading, but could move to Toulouse if the French bid is accepted.
The centre, which employs 150 people, collects meteorological data from around the world and develops short and long rang forecasts and models for EU member states.
A centre of the aerospace industry, Toulouse already hosts the National Centre for Space Studies (CNES), the forecasting services of French weather forecaster Météo-France and those of Mercator Ocean International, which is implementing the ocean monitoring service of the European Copernicus program.
France has already secured the hosting of the European Banking Regulator, which moved from London to Paris last year, and the relocation of several high profile banks.
French president Emmanuel Macron is keen to set up Paris as a rival financial centre to London after Brexit, and the French government has also been targeting British tech and computer games businesses.