US/CA Bachelor or French MiM to work in North America?

Hello,

I am currently a Law student (4th year) in France who wish to go to a business school, particularly to work in consulting.

I will obviously apply to the top French b-school (HEC, ESSEC, ESCP).

Still, my goal is to work in either the US or Canada for the first half of my active life (25-45years old).

Considering this important information, should I join a US/CA bachelor (would prefer to join either HEC Montreal or McGill in that case, as it is cheaper for French students) or a French master in management?

Even if I already graduated from law, I am considering going back to a bachelor program because I learnt the prestige of it is more important Than the master’s one: I could join a MiM in US/CA but wouldn’t be targeted by top consulting firms.

What do you suggest me to do?
Stay in France, study here, then applying for a Canadian consulting firm? (Is it even a thing though? [maybe in Montreal?])
Or go to North America to study in a bachelors degree?

I thank you in advance For your time.

Have a good day.