Months of the year in French

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Across
  1. 3. Is 8 months away from the end of the year (5)
  2. 5. Old Year's Night is in this month (8)
  3. 6. The end of the word is spelt the opposite of 'in' (4)
  4. 10. Begins the year(7)
  5. 11. The start of summer and the hurricane season. Also is the name of one of the characters in a Shakespeare play. (7)
  6. 12. The start of school (9)
Down
  1. 1. All Saints Day begins this month (8)
  2. 2. Is the middle of the year. (4)
  3. 4. The tenth month of the year (7)
  4. 7. Four months away from the middle of the year (7)
  5. 8. word (3)
  6. 9. Has the same name as a planet (4)
  7. 13. Sounds like the same month in English and like an