Csdrhrt

I moved to Quebec from Belgium 6 month ago,

I'm actually working as a consultant on a mission and everything was great until I had some disagreement with some aspect of the job, I asked to be moved to another mission but they said that I should take some vacation and come back cool headed (in retrospect, this was a good idea).

So on an impulse I started looking for a new job and accepted one after the interview process.
I didn't sign anything yet but agreed by email.

Now I regret my decision and I'd like to refuse quickly so to not waste anybody's time further.

I'd like to know if there could be any legal issue If I do so and the best way to formulate it.

I know it's unprofessional and feel embarrassed...

Thank you.

I didn't sign anything yet but agreed by email.

Depending on what is in the email and what is attached to that email you may have agreed to the provisions of the email.

If there are no stated consequences in the email then quitting as quickly as possible is the best course. The new company could be preparing for your arrival which can involve some direct and indirect costs. Acting quickly prevents those costs from growing.

Acting quickly also allows them to contact the next person on their list of acceptable candidates. The longer the delay the more likely the next choice has found a job.

To know if there are consequences you need to review all the documents you have been given and/or emailed. If you are unsure if a provision applies to you you may need to contact a local labor attorney.