The Sunday market is a must. Get off the Metro at Gambetta and go straight, you're there. Otherwise walk from the centre across Place de Republique down rue Gambetta and get more of the atmosphere. If you walk take a break at Le Stout for a coffee and cognac - it is the café on the corner with a bike suspended in the window. Then twenty yards later you are in the flower market and behind that the covered market. In the covered market there are plenty of treats.
A Polish stall which does the best smoked filet mignon in the world although a bit expensive at 27 euros per kilo. We call it 'baby' at home because it is so tender.
There is also a cheese stand that is good value and massive - so they always cut more than you want.
The other side of the covered is the open market. A mix of farmers' and bulk buy, but both are good value. Olives beside endives. The spice stands used to be good but they have doubled their prices recently. There is also haberdashery and second hand clothes and a fine selection of elephant-shaped underpants.
There is plenty to eat - banks of roast chicken, ribs, Chinese noodles and pies (try the cheese maroilles on a pie or traditionally dunked in coffee). All the cafés on the square are fine but I prefer those on the street on the side of the covered market as they are where all the stall holders go. In front of the church it is more trendy, very people-watching and people who have not been to bed.
There is a great family restaurant on the square but I'm not telling as they refuse to be in guidebooks. It serves a fixed menu of what is fresh and cheap. Fantastic veal liver, fish and chips (French style, no batter) and if the kidneys don't appeal there is a tender rump steak as standard. All this with a starter and a cheese plate or a dessert for 25 euros. Find it!
The market is on Sunday morning from 7am to about 2pm depending on the weather. If it isn't raining it is packed - the Lillois don't mind the cold, only the rain. France is very kid-friendly, but don't take a pushchair as all your kid will see are bums and you get stuck in pram jams.
Lots of other stuff to see in Lille: museums, medieval buildings, general Flemish architecture. A very under-rated place to visit.
or walk through the town across Republique and down rue Gambetta
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