Sugar 7: global search is not finding any results, even if Elasticsearch is ready and workable.

Hello everyone !

What i want :
Simply a fonctionnal Global search.

What i have :
Sugar Pro 7.5.1
My users need to search through Global Search, and we came to a strange situation :
Even if i search the name of a contact (wich is high boost), in the global search zone, i get a "No result found" little pop up.

What i did :
- I've checked in admin> global search if Elasticsearch worked. It is.
- i've clicked on "plan index", which gave me the little pop up described here : http://support.sugarcrm.com/02_Documentation/01_Sugar_Editions/04_Sugar_Professional/Sugar_Professio... but after a while, nothing has changed.
- So i've checked in the Schedulers, and there was no scheduled task which would perform the function::performFullFTSIndex job. I've added one.Called "test Index",  Active, as often as possible.
- Nothing happened too.
- I've checked in elasticsearch.log, and i have the following, which seems to be saying "it's good, the index is cool" :

[2015-07-07 16:24:58,683][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] creating index, cause [api], shards [5]/[1], mappings [][2015-07-07 16:24:58,733][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Leads]
[2015-07-07 16:24:58,799][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Contacts]
[2015-07-07 16:24:58,816][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Accounts]
[2015-07-07 16:24:58,828][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Calls]
[2015-07-07 16:24:58,837][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Notes]
[2015-07-07 16:24:58,854][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Contracts]
[2015-07-07 16:24:58,863][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [Cases]
[2015-07-07 16:24:58,885][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [de_Devis]
[2015-07-07 16:24:58,894][INFO ][cluster.metadata         ] [Thunderbird] [efa70bed4f2e5a75a907f99f7f153ca3] create_mapping [ag_ActesDeGestion]
- When going to my "test Index" scheduled task, there is no job running/done/queued nor failed.

Do you have any idea on what is happening in my global search, please?
Do you have some clue on where i have to search for the errors?

Thanks a lot for your time !