Updating to version 15.35 will get you up and running-or more accurately, up and limping. Version 15.34 and older aren’t supported in macOS High Sierra, and may not even launch.
Things aren’t as bleak for Office for Mac 2016, although they aren’t promising. As a reminder, after that date there will be no new security updates, non-security updates, free or paid assisted support options or technical content updates. All applications in the Office for Mac 2011 suite are reaching end of support on October 10th, 2017.