Just when you create the translated form you have to access your data base (the way depends on your host provider, here is through phpMyAdmin), note in the table UserDefinedForm the ID of the translated form, go to the EditableFormField, find the rows (a row equals a field) corresponding to the translated form and change their ParentID field to the ID noted before. That means that you will link the form fields to the page they belong to.
I hope that it applies to your problem and it helps.
Ah sorry, I did not understood. Don't take my word for granted, but I think the way Forms are displayed in SilverStripe (ie. div vs. ol) is not easily customisable through custom templates, at least it doesn't seem to be done directly with the code included in the userforms module.
Think about it: forms are everywhere from the CMS to the front-end login. They are rendered through the templates of the sapphire/templates folder and controlled by the sapphire/forms code. Dig in there if you want to modify your forms HTML structure.
I tried through phpMyAdmin, but I think that I have a problem. I found the ID of the translated form under UserDefinedForm, but under EditableFormField there is no separate entry for this new form. And if I add a field on the new form it gets added to the working french, original form!!!
After you add those fields to the translated form, no need to panic: if you see them in the original form is because they appear in EditableFormField with ParentID being the ID of that original form. Just change ParentID of all these rows and assign the ID of the translated form.
Ok, I got the translated English form created by changing the ParentID for every field like you said! However there one last problem. I was able to put in the data for the email recipients when I first created the translated form, but going back now to see why my form doesn't get sent anywhere the info is gone (actually it was added to the original french form) and I can't add it any more. It gives me the error "Not Found" when I click on the green plus under the "email recipients" tab.
I don't remember doing it myself, but if you look at the UserDefinedForm_EmailRecipient table, you'll see that the FormID field is pointing to the original form. Just replace the ID with that of the translated form and you'll be done. In my experience, once these ID fields are tightened up, you can modify the other ones through the CMS without going back to phpMyAdmin.