Yes, the two are CRM competitors, but Microsoft and Salesforce also are partners. (And almost were a single company, if reports of Microsoft's near purchase of Salesforce are to be believed.)
At Salesforce's Dreamforce conference this week, the two companies committed to integrate more of their products.
Salesforce and Microsoft announced an integration partnership last May. In October last year, the pair provided an update on their progress in integrating various Salesforce apps with Office apps and Power BI business-intelligence platform.
On September 16, the two announced general availability of the Salesforce App for Outlook, which works with Office 2013 and Office 365, and the Salesforce 1 Mobile App for Office.
The two companies also said they would be integrating Skype for Business and OneNote with Salesforce Lighting, which is the new Salesforce user experience that the company is bringing to its various products. The companies also plan to integrate Office Graph and Office Delve with Salesforce content. These new deliverables are due in the second half of 2016.
Salesforce also said it will deliver the Salesforce1 Mobile app for Windows 10 in the second half of 2016.
Salesforce had been working on a Windows 8.1 version of Salesforce1 Mobile, but ended up never getting beyond the preview stage with that app. Instead Salesforce officials said the company would focus efforts on building a Windows 10 version of that app.
(Salesforce did enable users to access Salesforce1 for Windows 8.1 via a mobile browser for IE 11.)