Salut,
That's not exactly how it works. I don't know if your familiar with regular expressions, but you can see what the system does exactly with the search query by having a look to the ADJUST_SEARCH_TEXT method of the CL_CRM_GENIL_ES class. Actually, it adds stars ONLY when a digit pattern is found. According to the comments in the code, this behavior has been set in place for ID fields, in order to handle leading zeros even if the user didn't type them.
So to sum up, when the system detects a number (by itself, I mean not in the middle of a word), it adds a "*" in front of it so that users don't have to type the leading zeros.
But when the developers did that, I'm not sure they thought about non-IDs numbers, like postal codes or telephone numbers, because there is no reason to take care of leading zeros in those cases.
Anyway, if I understood correctly, when TREX perform its indexing, it takes the fields that are to be searchable for a given object and concatenate them into one "big" string (I'm really not sure of this, but that's how I've been told it works). So if I'm not wrong, you were completly right when you said "there should be a search field available within your object where the complete address can be found, like "Hospital 13005 Marseille / France"".
That doesn't solve my problem :/ But maybe mastering the ESH Modeler would, so is there somebody skilled enough to tell me if it is possible or not?