Hello NN,

Thanks for your post here. I would like to confirm with you that the issue occurred in SharePoint Online or on the desktop application.

If it occurred in SharePoint Online, you can refer to the following steps to troubleshoot the issue.
1.Create a content type for a document template.
2.Add a new document template.
For how to add a document template to a document library, please refer to the following link:
http://office.microsoft.com/en-us/sharepoint-online-enterprise-help/add-multiple-office-templates-to-a-document-library-HA102409514.aspx .

If it occurred on the desktop, please try these steps:
1.Run Office 365 desktop setup .You can refer to http://onlinehelp.microsoft.com/en-us/office365-enterprises/ff637594.aspx .
2.Configure your Internet Explorer.
•Click Internet Options of Internet Explorer.
•Click Manage add-ons in the tab Programs.
•Select All add-ons in the drop-down box, and then check the status of “SharePoint OpenDocuments Class” is Disabled or Enabled.

If the status of “SharePoint OpenDocuments Class”  is Disabled, you can enable it.
If the status of “SharePoint OpenDocuments Class”  is Enabled, you can disable it, and open the Excel spreadsheet. It will be opened in the Office Web Apps . If it can be opened successfully ,you can enable “SharePoint OpenDocuments Class”. Besides, I would like to know whether you install the desktop Office completely. 

If there are any concerns about this issue, please feel free to post here.

Thanks,
Cherry Wang