Jazz festival food?
As others have said, the festival definitely serves up top-notch music, not food. ;-)
You will, however, be within walking distance of Chinatown for inexpensive and filling lunches & dinners & dim sum. Recommend Hong Kong (St-Laurent - roast duck & BBQ pork, Cantonese & seafood specialties), Beijing (de la Gauchetiere), VIP (Clark - good "Canadian" Chinese) and Mon Nan (upstairs on Clark - 3-course Peking duck specialty) and Lotte Furama (upstairs on Clark - dim sum specialty).
As others have also said, the jazz fest is held right downtown and you'll be within a walk, metro ride or short cab ride away from the best of what Mtl has to offer, so don't fret.
> what are the can't miss foods of Montreal?
There are some great threads covering this topic. Here are a few you may want to check out:
Inexpensive Places Not to Miss
Best of Montreal
More potentially annoying Montreal questions
Another tourist here
The Ultimate Montreal Experience
That should give you somewhere to start. If you're interested in anything specific, let us know!
Short answer: no.
Slightly longer answer: As the only things served are by 'sponsors of the festival' quality isn't exactly part of the equation, and whatever you eat or drink, it won't be cheap.
That being said, Heineken is an acceptable beer (better than Blue Light). These are the links to the various food sponsors at the festival:
Ice Cream: http://www.vitalinkevents.com/
The Cheese sponsor doesn't have a website.
There will be a Kiosque Louisianais, a Barbecue, a Fruiterie Soleil et Fraicheur, a Bistro SAQ, a Sandwicherie, a Friterie, hot dog carts, a Terrasse Mexicaine, a Terrasse Amarula, and some other things along those lines.
In short, eat elsewhere and enjoy the music on site.