In terms of UK citizenship (England/Scotland/Wales/Northern Ireland), it can only be passed down to one generation born abroad, so unless one or both of your parents is a British citizen, you will not have any claim to UK citizenship.
For Irish citizenship, I believe it can be passed down through two generations, so you might have a claim to Irish citizenship if you have either a parent or grandparent who is an Irish citizen.
I don't know much about the French citizenship laws, but doing a quick online search, it looks like you might only be able to claim French citizenship if one of your parents is a French citizen.
If you're looking into the Ancestry visa for the UK, that is a visa that is only available to Commonwealth citizens who have a grandparent who was born in the UK, so you will not be able to qualify for it unless you hold citizenship from a Commonwealth country (i.e. Canada) AND one of your grandparents was born in the UK (See:
http://www.ukba.homeoffice.gov.uk/visas-immigration/working/uk-ancestry/).