Not a lot here to go on. Francis is not a common Mackay name - there seems to be two possible areas for you to search. There was generations of this name born in Bothwell, Lanarkshire beginning in 1720 or I notice from the IGI there are many generations of the name in Caithness beginning from early 1700. Both these areas have links through Cyndie's lists for Scotland. Link to that from the links on Highland Hearts.
Hope this helps.
Christine