there are six Peter Smith entries included in Griffiths Valuation (1850-1860s) for Co. Leitrim - see :
http://griffiths.askaboutireland.ie/gv4/gv_family_search_form.phpSurname/ Forename/ Placename/ County/ Parish
SMITH PETER DERRYGOAN LEITRIM DRUMREILLY
SMITH PETER DRUMCOURA LEITRIM DRUMREILLY
SMITH PETER DRUMANY LEITRIM OUGHTERAGH
SMITH PETER CORRIGA LEITRIM CLOONE
SMITH PETER TOOMAN LEITRIM CLOONE
SMITH PETER TOOMAN LEITRIM CLOONE
The website includes details maps showing details of these
this is a land valuation and only includes heads of households.
As Francis birth was about 1854 it is too early for Civil records which started here is 1864. Parish transcripts for county Leitrim are included in the (pay-site) of the Irish Family History Foundation at
www.irish-roots.ieI had a quick look at the index and there is one match for Baptisms of a Francis Smith (between 1850 and 1858) and this in 1856. (not certain thatthe father is Peter though..)
there are also about 4 possible marriages matches for Peter Smyth between 1844 and 1857
Shane