I have registered for a training which is going to be organized in Germany. The registration was done by a form in which I have mentioned my personal information, my address, and the company I work for. The problem is that I have submitted the form without reading the conditions where some cancellation conditions were mentioned. The manager sent me an expensive invoice and he asked me to pay it even if I am not going to attend the training. All want to know is what will happen if I don't pay the invoice and just ignore their emails. I haven't signed any document, all I did is I answered some of their email telling them I am sorry for not replying to your emails and I am not able to attend this training.
It will depend on the exact language on the registration form that you submitted, but it may well constitute a contract. A physical, pen and ink, signature is not required to form a contract, and online document can do so, provided that there was agreement.
If the form created a contract, you are probably bound by the terms, subject to any limits in law. If cancellation is not allowed, or allowed only under circumstances that do not apply, you may be liable for payment.
If you just ignore this invoice, the organizers could sue you, with a plausible chance of success.
You would be wise to clearly tell the organizers right away that you wish to cancel any reservation, and that you never agreed to the price they wish to charge. That should put you in the best possible position to dispute any charge.
The organizers might not choose to sue you, particularly if you have given them reasonable notice of your intent to cancel. But you cannot be sure of that.
There may be laws in Germany or France which require the organizers to give you a chance to cancel. I do not know if such laws exist, and if they do, what their provisions are. They might well be limited in time.
You could claim that since you never agreed to the price, no actual contract existed. The sooner you indicated a desire to cancel after learning the price, the better this argument will be. You may need to consult a lawyer on the best way to make such an argument.
Ignoring this invoice is a very bad idea. But it is a good idea to check if there is a valid contract and if you can get out of it. If you "signed up" to the training online, you may benefit from consumer protection regulations on internet sales.
You are in France, the company is in Germany, right? Check which law applies. Either way, it would implement the relevant EU regulations.
It might be a good idea to talk to a real lawyer, not some guys on the internet.