Mme... lived in the 16th Arrondissement, which is quite the oh la la place to live. Looking at the old address, I see that her 5 story, 7 bedroom town house had been converted to separate apartments. Anyway, it was a single residence when I was there and my room was on the top floor! Oh how I loved my view out the high window overlooking the rooftops of Paris.
Mme. was a wonderful cook and she took every opportunity to tell me the correct (French) way to eat foods. Never cut the lettuce with a knife and don't cut off le nez (nose) of the cheese triangle! She made wonderful lamb (which I ate at home about once a month anyway), cakes, fish, vegetables, etc. If it was classic French, she made it (and I ate tripe but not too fond of it). She had an old crock in her kitchen where the last bits of wine from the bottle were poured. This was for making vinegar.
Her meals usually had an appetizer, entree, salad, cheese, bread and sometimes a small dessert. She knew that I had a sweet tooth. Even if it was fruit, that would suit me fine. Many times, I was able to watch her prepare food right before serving. This is where I learned to emulsify the salad dressing (my Greek family never emulsified it), and make an omelet. It's difficult to write down the process, but there is one that she used. It's quite an arm workout to do it properly.
One of my secrets is to have one pan that is totally designated to making eggs. Nothing else gets cooked in that pan. Start with 4 eggs and beat them well, adding herbs if desired. Put a pat of butter in the bottom of a hot pan, not so hot that the butter browns though. Add the eggs all at once, and with the flat part of the fork against the bottom of the pan, shake the pan as you mix the eggs. This will make it where there are no large chunks of egg in the omelet (that would be a country style omelet... which is good too), but it is velvety smooth. After mixing the egg, tilt the pan so that the egg goes to one side of the pan, add extra cheese, and invert onto a plate.
A more rustic way to cook an omelet, which is easier in my opinion, is to add the eggs into the hot butter (yes, use butter not oil or bacon fat), pour in the eggs and as it starts cooking, gently slide the outside portion towards the center of the pan, keep doing this until most of the egg is cooked, yet still runny in the middle, if that makes sense. Add cheese, veggies, and meats if desired, and tilt out onto a plate. In either case, I remember that she did not brown the omelet as is sometimes done. I think the key is not to fully cook the egg before you plate it, let it be just a little "soft" in the center. I think browning the omelet toughens it somewhat. This may not be the "Classic Method" taught at cooking schools, but it was classic at her house.