How to specify a Custom Message in the New Mail Alert

Do the following:

   1.   On the Home tab, in the Move group, click Rules, and then click Manage Rules & Alerts...:

   2.   In the Rules and Alerts dialog box, click New Rule...:

   3.   Outlook launches the Rules Wizard. In the section Stay Up To Date, in Step 1, select Display mail from someone in the New Item Alert Window:

   4.   In Step 2, click people or public group and enter the addresses that you want this particular alert to appear for. Then click the Next > button:

   5.   Click a specific message and enter the text you want to appear in the Alert Message window, then click the OK button:

   6.   Click the Finish button to save the new rule.

See also this tip in French: Comment spécifier un message personnalisé pour la notification du nouveau message.