Le Fromentier is a beautiful and somewhat hidden bakery on Laurier Est, just east of the park. We definitely enjoyed some tasty flaky breakfast pastries from this shop. The highlight was the chestnut (marron) pastry.
Looks like they carry a great selection of savoury and traditional breads as well. I would rate the quality as high but not excellent. Their puff pastry doesn't have the delicious buttery pop that one finds in the very nicest puff pastries.
Prices are quite reasonable, and it appears there's a combo cheese shop adjacent. Bread and cheese sounds like the perfect combo for a picnic in the park.
Pay attention to the address, it's down in a basement and very easy to miss.