A workaround solution was pointed out by Lemonstand.
When you send the invoice for the manual order to the customer, send the link to yourself and/or simply change the Invoice Checkout link by adding the following at the end of it ?locale=fr-ca for French and ?locale=en-ca for English.
I am trying to do this but it only works for me when I’m already logged into shopify. It just redirects to the homepage when I am in private mode. So dont think the customer will be able to open the link.
Any other solution?