Scenario
Your signature template uses a custom font stack, such as Calibri, Candara, Segoe, Segoe UI, Optima, Arial, Sans-Serif
However, once the signature is received in Outlook, the fonts turn to Times New Roman or similar serif font.
Reason
Outlook adds 'single quotation marks' to the first font in the list, causing this issue. You can view this in the source code of the email as well: 
Resolution
To resolve this issue:
- Add "double quotation marks" around the first font in the stack to override the marks added by Outlook and force the font to remain as a Sans-Serif.
For example, the font stack will look like "Calibri", Candara, Segoe, Segoe UI, Optima, Arial, Sans-Serif: