I've never found Filemaker terribly friendly for calendar-type stuff, but maybe that's just me. You could try http://www.seedcode.com/cp-app/ste_cat/sccalcomplete for their calendars etc written in FM.
Or google for 'Outlook Connector Filemaker'. You definitely can buy plug-ins that will link Outlook and Filemaker.
Are you wanting to send them an email based on a date the user enters into the system? (Don't really need a calendar for that.)
It's possible to write a script that runs once, the first time a file is opened that does a find for such reminder dates and uses send mail to send out emailed reminders.
You have to build sufficient intelligence into the script so that reminders like this don't get sent more than once but that can usually be handled by the script modifying a field in the record to record the fact that the email was sent. (Your find then uses criteria that will keep from finding records where the email was already sent.)
Outlook has been an option for email clients for windows for some time now. With the recent release of the 11.03 updater, Mac users are also supposed to be able to send email via outlook.