Hello Melancolique. Yes, 'je souhaite' does mean 'I wish' and is used in expressions like... 'Je te souhaite
bon anniversaire' = 'I wish you a happy birthday' 'Je te souhaite bonne chance' = I wish you good luck' If you want to say something like 'I wish you would tell me why......' or 'I wish Paul were here', then you need to use 'je voudrais que' 'Je voudrais que vous me disiez pourquoi...