Ask them what life was like when they were young? I remember my mother telling me about the horse and buggies when she was young and when the first street cars were installed.
If they remember, ask where they lived. If they aren't around to ask, I went to our public library where they have City Directories back to the early 1800s. By going through these directories from around the time my great grandparents came here, I was able to narrow down their date of arrival in the area. Our City Directories list the names of the adults, addresses, where they worked and what kind of work they did. If they died before the next year's directory was printed, it tells of that person now being deceased. Lots of information can be found here for the looking.
Other questions you might want to ask is what kind of schooling they had; where did your parents, grandparents and other family members meet and how. What do they remember about their parents and where they came from. What were their parents full names, dates and places. What was life like for them and who were their brothers and sisters. Who were they married to and are any of them still alive - if not, when did they die.
You might find that at first, your elderly relatives might have a hard time remembering but your interest will like spark them to begin thinking about the past and you might come up with some interesting tidbits to boot. Now it doesn't mean that everything they tell you about people, dates and places is 100% accurate but that becomes part of your search to verify all of the information they give you.
If you can obtain such tidbits on family history, it will enflesh your family history. Names and dates are important but to have the history to go with it is just marvelous!
From this point on, it is pure research. If you are of Acadian or French Canadian descent, if there is one near you, you should join an American Canadian or French American Genealogical Society. Usually, they have copies of parish registers in book form or on microfilm that will help you find all of your ancestors in Canada once you get back to the last couple to have married there before coming to the United States or other countries. Once in a while, you might hit a glitch/brick wall but by far and large, if you are able to research in marriage records for Canada that a genealogical society provides, you should be able to research your family lines back to the first ancestors who arrived in Canada from France for example. Once you begin to take your family lines back from generation to generation, it really becomes a quest for more information! It's a challenge but a very rewarding one in the end.