A combination of strong bulk shear (over 35 kt in the 0-6 km layer) and over 1000 j/kg of SBCAPE may yield potentially severe thunderstorms in E and C ON on Monday and S QC on Tuesday.
500 mb temps are progged to be around -20 C in the left exit/entrance area of a H5 jet streak on both days, indicating a very strong cold pool for late May. Large hail and lots of it is definitely possible given the low freezing levels (only 2-2.5 km AGL) and PWATs near 25 mm (which should support heavy convective precipitation).
As stated, lots of precipitation is expected but storms may produce little in the way of rainfall and produce accumulations of hail.
The freezing level in this sounding-depicted column, just south of Montreal on Tuesday, is only 250 mb AGL. I believe that the infamous southern Alberta hailstorms develop in environments with similar freezing levels. They can occur with low CAPE and low bulk shear values as well.
Strong to severe wind gusts are also likely in thunderstorms. The strength of the wind gusts will depend on the strength of H7 winds as dry air entrainment appears to be marginal but at the very least, 70 km/h gusts are possible.
Monday, May 29 is also the 30th and 31st anniversaries of some of the worst hailstorms to hit Montreal and surrounding areas. The first May 29 hailstorm produced baseball-sized hail in Possum Lake during what is remembered to be an active period for hail (80s and early 90s). On the other hand, large hail became rare in the 2000s and early 2010s, before recording a large hail day in 2015 and two last year (one of which yielded golf-ball sized hail; probably the largest in 25 years).
When adjusted for inflation, the 1986 monetary damage figure is now equivalent to over $91 million, which is still less than the Canadian hailstorm damage cost record of $400 million in Calgary, set in 2010. Damage figures with the same storm today would probably be well over $100 million when taking into account the urban sprawl and population growth on the south shore of Montreal which was the primary target of the storm.