Directly.
Until the end of the French- Algerian war, Algeria was an overseas colony of France .
Why was Monet sent home from Algeria?
Claude Monet left Algeria just a year later in 1862 when he contracted typhoid fever. Normally a young soldier would have expected to remain in the army for seven years, so who would pay the army back in Monet's case? Fortunately the artist's aunt, Madame Lecadre, saved his hide and bought her nephew out of the army.
Perhaps he hoped a posting to Algeria (near enough to Morocco) would enable him to study the special light, exotic subject matter and heightened colour that could never be found in France. Monet was shipped off to Algiers in June 1861 where he went through military training and work with horses.