Also, verify with FEDEX how long you need to work with them before being able to travel (sometimes 6 months) and who can travel, your parents might not have benifits on any/all airlines.
I think you get better benifits with Delta but again, you need to review your travel program. Also, due to weather this time of year is much easier to get to/from Europe than summer time, May is iffy as people try to nonrev before the summer crowds start.

Post back with what your flight benifits will be and it will help with figuring things out.