Joining two tables with unrelated where clauses
LEFT JOIN one subquery to get the maximum of FTE per employee and another to get the maximum (or minimum, ...) assignment for each employee and FTE.

SELECT e1.*,
       a4.*
       FROM employee e1
       LEFT JOIN (SELECT a1.employeeid,
                         max(a1.ftepercentage) ftepercentage
                         FROM empassingments a1
                         GROUP BY (a1.employeeid)) a2
                 ON a2.employeeid = e1.employeeid
       LEFT JOIN (SELECT a3.employeeid,
                         a3.ftepercentage,
                         max(a3.assignment) assignment
                         FROM empassignments a3
                         GROUP BY a3.employeeid,
                                  a3.ftepercentage) a4
                 ON a4.employeeid = e1.employeeid
                    AND a4.ftepercentage = a2.ftepercentage
       WHERE e1.enabled = 1;