Moving to Montpellier, France

Yes french bureaucracy is a nightmare.
Try looking on le bon coin. It’s a website where people can advertise renting their apartments.
Going through an agency is going to be hard as you’ll need a lot of french paperwork.
I experienced something a bit similar when I came over. Even though my partner has a job, a guarantee and the funds we got turned down by a few agents because of my lack of paper work and the fact that as I didn’t have a wage at that stage we didn’t earn three times the rent which you often need to prove.

Thank you for your response.
I will look into leboncoin.fr.
Hopefully I will be able to find something soon.
Best regards.

To get a French bank account, consider renting an Airbnb place for a month - use that address and landlord's ID and justificatif de domicile.
Once you have the account, transfer a good chunk of money. You may need a caution (a year's worth of rent in escrow - *not* used for rent tho!)

Finding a rental during winter is difficult - landlords can't evict between Nov 1 and end of April.
You can try looking now for something available May 1, since several months of notice is required to move.