Literally, 'busy yourself with your onions' ie 'mind your own business'.
I find myself minding my French onions (in both senses probably) most days. Proper French yellow Mulhouse type onions are my favourites for cooking. They are often a flattened sphere rather than bauble shaped and are usually a bit more expensive than other types. I don't know what exact variety they are as a general rule in the shops, but we grow one called Stuttgarter Reisen which seems to be what is commonly available in the garden sections of the local bricos. They look exactly like these ones that I bought at the market, and perform very well if we get some rain (as opposed to none at all in their growing period last year).
These onions are very much sweeter than their round rivals and make by far the best onion gravies, tarts and marmalades. They are a bit softer at the stem end, so don't have quite as good a storage life as hard round onions and for that reason are not generally exported. If you want real French onions outside of France you will probably have to grow your own.
They are called Mulhouse onions after the town in Alsace where they were developed. Mulhouse (pronounced 'moolooz') has an annual onion festival in September at which you can eat your fill of onion soup and onion tart. The town's other claim to fame is the remarkable Automobile Museum.