The probation period in several European countries works both ways.
Usually contracts also cannot subtract rights that are written in the law, and such clauses can be indeed deemed illegal in several countries.
I would never accept a one-sided probation period nowadays. On the other hand, I was an expat a few years, and I know first hand that it can be customary to apply one-sided probation periods for people going abroad for covering their investment. However I was working in Africa, and I am confident quite a few European countries enforce a dual sided probation period. I would let it go and accept the probation period because you need to focus on other issue.
A six month notice period is pretty abusive, and again almost all the same comments apply, excepting that is not that common. In practice, if enforced, it can deter you from changing positions. Most employers arent willing to wait six months for a new prospective hire. Try to negotiate it down to at least 3 months if it is not common to your industry.
You are not obliged to accept all the terms on a proposed contract and you can and are expected to negotiate it; if in doubt, talk with a lawyer specialised in European work law.
Be aware how the six-month notice clause is worded also. Depending on the wording, it might prevent you for getting another position for a significant period of time in the remote possibility they use the probation period. Or it might hide a non-compete clause in some other legalese.
Ask for a copy of the contract(s) before signing them and show them to a lawyer instead of asking random people in the Internet.
I also agree with the comments bellow the biggest no-no on this contract is the lengthy notice period; do not sign anything you might regret on your future.
If hired in the US by a firm with an American subsidiary:
- You probably will have an US and you must have an European contract;
- ask for both legs of the contract to show a lawyer, both the US and the European one;
- Do not believe the white lie the European contract "will be just a formality";
- Beware of clauses in the US contract deemed to get around rights given by European labour law.
I would consult a lawyer if I were on your shoes; I did not before signing my expat contract, being younger and more naive, and had it gone wrong I would be in big troubles (yeah, that kind of clauses "it never happened to us"...it sure did happen before, people gone sick, people that did not adjust well to the new country, people gone berserk with the new environment getting into drugs and drinking as I found out later through the grapevine ).
Finally, a prospective employer talking you down about clauses of a contract is an huge red flag that should not be ignored. Remember, HR are not your friend.