I think that French always use article before word, so when the speak about tradewind they probably say 'l'alizé'. But Alizée is just french female name (not very popular), I think that they aren't wondering about that
Now part "Did you know?"
Alizé is also 'nickname'(?) for French anti submarine plane - Breguet br.1050 Alizé (constructed in 1960)