Are you French enough?

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Across
  1. 6. actual French president
  2. 7. brotherhood color during revolution
  3. 9. classic famous hat
  4. 11. second biggest city
  5. 12. monarchy’s color
  6. 13. French bread
Down
  1. 1. French pastry
  2. 2. famous French author
  3. 3. D-Day beaches territory
  4. 4. famous French monument
  5. 5. robbed museum
  6. 8. capital of France
  7. 9. revolutionary color
  8. 10. mountains between France and Italy