Yes I believe there should be a cooling off period but I would contact the dealer first thing.
Renault dealer tried to get my 20 year old daughter to sign up for one of these on a new Twingo 4 years ago, she had enough deposit for half the car and just wanted to finance the rest over 3 years, he was very pushy so I guess they make plenty of money on the finance deal.
That was all he wanted to talk to her about - just put £1000 down, keep the other £3k in your account that sort of thing until I went in with her looked at the details and took a bank loan out for her in my name for the balance. 4 years later she has now owned the car fully for a year, had she gone down the dealers route she would she be having to find £4k and I would imagine that £3k he said keep in your bank would have been well gone.
See if you can get a bank loan, they are much cheaper than dealer finance unless you can truly get a 0% deal.