Kepis are usually dark colored and can use a wimple to shield the neck from the sun in arid climates. The white hat which is worn by not just the French but many militaries and service groups is the pith helmet.
Sorry, mehaul - but your link doesn't support your answer. The article mentions a number of armies who have worn the pith helmet, but never mentions the Foreign Legion.
CmdrK's link shows a photo of the white kepi on a Legionnaire.