For births, deaths & marriages 1750 - 1850 you have a choice. Protestant marriages 1845 -1850 will have been recorded with the GRO but otherwise no statutory records will exist for any other event. So you'll have to rely on church records.
From this chain it appears that the French families in Randalstown were a mix of Presbyterian and Roman Catholic.
Catholic records are available on microfilm in the National Library in Kildare St, in Dublin (website :
http://www.nli.ie/). Presbyterian records will be with PRONI and probably also with the church (note that there are 3 Presbyterian congregations in Randalstown - OC, 1st & 2nd). And you might also get extracted records on Familysearch.
Elwyn