Hello lmhiggins ,
As has been mentioned the Higgins name is very common in the Kilmovee Parish. However the name Francis Higgins is very unusual and there are only three instances of it occurring as a groom, baptised child or witness to a marriage or baptism between 1854-1910 for baptisms and 1824-1910 for marriages. Christian names were as important as surnames in identifying lineage. It was only mid to late 1850’s that townlands were included in the Catholic Parish records so a little bit of faith is required with the details provided below.
The earliest record of a Francis Higgins is a marriage 1832 Dec 23 to a Sarah Forry, as shown in the parish registers http://registers.nli.ie/registers/vtls000632349#page/17/mode/1up . The name Forry is a little easier to deal with and from the Griffth Valuation the name is only associated with two townlands Tavraun and Cloonfeaghra which are both in the western part of the parish around the Urlaur area.
From the parish records for the period above the only additional townland name which appears is Shanvaghera being associated with the Forry surname. It could be easy to confuse this name with a similar townland in the parish of Knock, but as often happens communities were the preserve of many names which were dispensed with following the pre 1851 reorganization of townland names and continued to use them at a local level.
The only reference I could find with Shanvaghera associated with an area in the Kilmovee Parish was a pension application for a Mary Feeney (nee Foroy) as detailed in the link http://censussearchforms.nationalarchives.ie/search/cs/results.jsp?censusExtractYear=&applicantSurname=foroy&applicantFirstname=&applicantAddress=&fatherSurname=&fatherFirstname=&motherSurname=&motherFirstname=&county=Mayo&barony=&parish=&townland=&city=&search=Search
This would suggest that Shanvaghera was indeed part of the Tavraun/Tavrane townland of Kilmovee.
The only other two mention of a Francis Higgins in the Catholic Parish records were:-
Marriage - 1856 Nov 2-Francis Higgins to Maria Higgins-pt-Daniel Higgins,Bridget Higgins
Baptisms 1908 Aug 29-Kate of Dominick Lavin and Ellen Roddy-sp-Francis Higgins, Mary O’Hara-Clooncara
To give you an idea of the locations menioned I have used google maps to assist.
Cloonfeaghra, Kilmovee to Tavraun, Kilmovee
https://www.google.co.uk/maps/dir/Cloonfeaghra,+Mayo,+Ireland/Tavraun,+Co.+Mayo,+Ireland/@53.8652268,-8.7868921,14z/data=!3m1!4b1!4m13!4m12!1m5!1m1!1s0x485eac7a89fc589b:0x13c9681fed7ac6f0!2m2!1d-8.7756184!2d53.8573921!1m5!1m1!1s0x485eac4036966b19:0x8eebdc8dbfc9b69a!2m2!1d-8.7649309!2d53.876364
Cloonfeaghra, Kilmovee to Shanvaghera, Knock
https://www.google.co.uk/maps/dir/Cloonfeaghra,+Mayo,+Ireland/Shanvaghera,+Co.+Mayo,+Ireland/@53.8420485,-8.8951876,12z/data=!3m1!4b1!4m13!4m12!1m5!1m1!1s0x485eac7a89fc589b:0x13c9681fed7ac6f0!2m2!1d-8.7756184!2d53.8573921!1m5!1m1!1s0x4859548b4554e21b:0xa616bf4bb55d4695!2m2!1d-8.8858958!2d53.82229
In conclusion I would suggest based on the fact that pre 1850 there were three churches in the parish , the Francis Higgins and Sarah Forry would have lived very close to each other and used the Church at Glentavraun rather than the old Church in Ballyglass/Rusheens in Kilmovee Parish. If you are to proceed with DNA testing this hopefully will aid in narrowing down the focus of which of the many Higgins branches you may belong to in the Parish.
Good Luck.