It depends. Student lawyers go to multiple lectures to understand contract formation in one part of one state in the EU (England and Wales are part of the United Kingdom, but contract formation is different in Scotland). The law will be different in other parts of the EU.
It also depends what the contract is for. As a specific example, that might not be enough to form a contract for the sale of land in E&W (such a contract has to be in writing, and I'm not convinced that filling in a text box would count).
Finally, are you sure you want to form the contract then? Most online retailers say that the contract is not formed until they dispatch the goods; until then, the customer order is just an offer to form a contract. That way they can't be sued for specific performance if they turn out to be out of stock - they can just turn down the offer and return the money.