Well, I have more than one sister, so I call the eldest one "big sister", the second eldest "second sister", the third eldest "third sister" and so on. This also applies to brothers, uncles, aunties and cousins, so I have people to whom I call big uncle, small aunt (the youngest aunt), third cousin... And since in Mandarin we have distinctive words for people older or younger than you, people from parental side or maternal side, it is easy to know the relation between two people, if they are related by blood / marriage.
In France, just like in Asia, people address parents and grandparents by their title , but for everyone else in the family they simply call them by first name or last name. It used to be very confusing for me, as when a friend introduced me to, say a cousin, I didn't know if this cousin is from the parental or maternal side, or if he is older or younger compared to my friend. And, it took me some times to accept calling my parents in law by their first name, which in my culture is considered very rude.
There is also a practice that surprises hubby and my MIL : the first thing we say when we meet someone. In France, it would start with a bonjour or salut. In my family, the younger generation has to call out to the elder generation by their "title". For example when I go to my sister's house, my nieces and nephews have to call me "bei yi" (last aunt in Hokkien). And I have to call out to my sister and my brother in laws because they are older than me. Well, how about hubby? He gets to have special treatment as everyone calls him by his first name, else he would be called "bei yi tiung" (last aunt's husband in Hokkien).
When I was a kid, whenever we went to visit someone, my mother would make sure that I addressed everyone in the house (aunt or uncle if not blood/marriage related) before I was allowed to go. Naturally, I try to train Aelig to do the same. But I forgot that in France they don't practice the same things! When Aelig went to visit my office for the first time, I introduced one of my coworkers to her by saying : this is tonton M (uncle M). This coworker immediately laughed hearing me addressing him as tonton (uncle in French). Later he told me that only his siblings kids would call him tonton in France. You just don't go out and call everyone older than you tonton or tata (aunt in French). I was very embarrassed.
Back to my MIL's comment. I was surprised on how she feels about it. I actually love the way I call my sisters very much. Example, let's say my sister's name is Marie, and I tell people that I went shopping with Marie, this could be any Marie, nothing so special. But if I say I go out with my big sister, that's special, because in the whole wide world, I have only one big sister. Besides, elder sisters would usually take good care of their younger sisters.
From my observation, France has its unique practice as well in addressing family members. It goes back to the confusing vous (polite form of you) vs tu (informal form of you). When I asked my French professor how should I address my MIL, she said she would never use "tu" as it is impolite. When I arrived in France, my MIL was disappointed when I use "tu" with her as she thought that I wanted to keep distance between us. So now I use "tu" with everyone in the family, including the grandmothers, to show that I want to be close to them. And then I notice a weird phenomena : everyone in the family would use "tu" with each other except the son in laws. The son in laws use "vous" when calling their MIL. Are they trying to keep distance? How about the neighbors? I feel so close to them so I use "tu" with them but everyone in my French family use "vous" with them. That's something hubby couldn't really explain, just like I couldn't explain to him why Chinese bothered themselves with so many kinship terms to address different family members.
For those who are interested, you can watch a Youtube video about Chinese Family Tree here: