Drumcliff is the name of the Catholic parish that covered Ennis town, and they have transcripts of their records online - see : http://www.ennisparish.com/genealogy/
The marriage of Patt and Jeane appears with the date you mentioned. The actual register would usually include names of witnesses, and possibly place of residence for one of the couple. Parents names would not usually be included on a marriage record for this timeframe.
EDIT : RootsIreland (pay-website) have transcripts for Ennis/Drumcliff in their system, but just baptisms so far. They only started to add records for Co. Clare recently, so might be worth keeping an eye out for an update for their system with marriages ..