Offer to buy

No, you can't. The owner can go to court and force you to buy. If you're lucky, you'll just loose your 10% deposit.

See a lawyer.

Now.

Depends. If the reason why you would like to withdraw is not being able to secure a mortgage, then it is accepted by law. However, if you for some reason just changed your mind, im afraid you are bound with your offer.

I agree with J - talk to a notaire.

Second to see a notaire ASAP!

Second also KC above: the only (semi) legal option - but only if this sentence is written in your offer!!!! - that your bank refuses your mortgage and confirms this in writing. if this sentence is not in your offer and your seller is not willing to accept your withdraw = 10% deposit to be paid & end of story.

"I made offer by email".
That is 'in writing'.

Whether or not you have actually paid a deposit is irrelevant, you are still liable to pay 10% of the offer if the seller forces the issue.
Also, 'not being able to secure a mortgage' means that literally - it does not mean 'not being able to secure a mortgage from the bank of your choice at terms which suit you'. It means that no-one, anywhere will give you a mortgage.
The only exclusion is if the offer specified conditions about a mortgage and if those conditions were accepted by the seller.

As KASSEISTAMPER notes above, your offer was in writing, it was an e-mail.
Personally I would speak to your notaire immediately.
You do have a notaire don't you, presumably you spoke with him before you made your initial offer?

Please let us know what the notaire says.

I'm under the impression that nothing is binding until the compromis de vente is signed.

There was a case recently where an SMS was deemed binding.
If you made an offer by email, it implies that it was a firm offer, and it makes perfect sense for the seller to accept it, so even though there's no written evidence, I think the fact that you sent an email would stand up in court.

A verbal contract is binding. You say you offer X and the seller says yes, then that's it - there's 4 months for the sale to go through. The problem is that proving that the conversation took place, but given that there's an email, that's it.

However, if the seller didn't reply formally, maybe he'll accept you withdrawing the offer. Don't be surprised if it prompts him to send a reply though.