No
Why? Because you should be inside at home! #StayHome
But if you absolutely had to go out to get groceries, medication or other essential travel, Yes, you do need a jacket.
Why? Because it's not very warm out.
Based on the weather in Montreal, QC, Canada as of June 1, 2020 2:53pm local time.
Now
Light Rain
Temp: 57°F14°C
Wind: 13 MPH20 KPH
Precipitation: 100% rain
Temp: 57°F14°C
Wind: 13 MPH20 KPH
Precipitation: 100% rain
Today
Next 2 hours: Yes
Next 4 hours: Yes
Next 8 hours: Yes
Tomorrow
Yes
Light rain in the evening and overnight.Low of 46°F8°C, High of 66°F19°C
Wind: 4 MPH7 KPH
Precipitation: 60% rain