With a fixed price contract, the PM will need to tightly control scope -- be sure the requirements are as well defined as possible before committing to the project, changes are well documented, and there is no "gold plating" (essentially exceeding requirements which can put the project at risk).
Of course these would be best practices for managing any project, but the Project Manager will need to be more vigilant around these areas for FP.
In addition, there should be a focus on tasks in this priority order:
Critical Path Tasks
Near Critical Path Tasks
Tasks with Least Slack
Tasks with Longest Durations
Tasks with Most Resources
Tasks with Least Resources