Place of burial depends on several factors such as religion and place of origin.
If Church of Ireland then check local Church of Ireland burials (may not be online); if Presbyterian then check both COI and Presbyterian churches (most Presbyterian churches don't keep burial records but there may be a headstone). If Catholic then check for headstone at local Catholic church.
There was also a Methodist Church in Portaferry-
http://www.lennonwylie.co.uk/PT1901OP.htmHowever, if Francis was from somewhere outside Portaferry he could be buried in a family plot there.
Irish News & Belfast Morning News, 6 May 1902: County Skipper Browned Liverpool. Captain Smith, of Portaferry, master of the schooner Mary Ann, belonging to Mr. Elliott, that place, was accidentally drowned at Liverpool Saturday …
I may be looking at a different Echo report but it gives his address as Shaw Street, Portaferry.
Not sure that there was a Shaw Street in Portaferry
and I can't see a Shaw St. listed in 1901 Belfast directory