Is a verbal agreement to start the hiring process with a German company in Germany binding by the German law? In other words, does one have to sign the contract once it is ready?
If two parties agree to the terms of an exchange, then there exists an enforceable contract. A signature is not needed to create a contract.
However, an intent to negotiate a contract is not, per se, a contract. Absent some specific and explicit measures (which for major deals may be codified in an MOU or LOI that itself contains contractual terms), if you can't reach an agreement on terms then there is no contract.
It's up to the particulars of "the verbal agreement to start the hiring process" whether an agreement on exchange has been reached, or merely proposed. E.g., "You and I agree that I will pay you $X in exchange for Y due Z" is a contract.
"You and I agree that we'd like to work together, and we'll hammer out the terms X, Y, and Z by the end of the week" is merely a proposal to contract, not an actual contract. Of course, this doesn't mean you're immune to liability for failing to reach a contract in this hypothetical: you can always be sued!
Verbal contracts are valid in Germany, but in reality can be very hard to enforce.
In the example of a hiring contract, the 2 parties may have different agreements in mind when shaking hands. Imagine a situation where one party shakes hands with the intention of actually hiring the other person, while the other person thinks the handshake is just an agreement to send the actual contract for review and possible acceptance - these people didn't agree on the same thing, so the contract is invalid.
And even if both parties had the same agreement in mind at the time they shook hands, good luck proving that.
In Germany a employment contract is validly agreed on without any special form, verbal and even impliedly. But this holds only true, if the parties really agreed to bind themselfes by a contract. Section 154 § 2 BGB (semi-official translation) helps us:
If notarial recording of the contract contemplated has been arranged, the contract is, in case of doubt, not entered into until the recording has taken place.
The translation is not so good. What is here translated as "notarial recording" ("Beurkundung") includes also written form (a signed document, section 126 BGB).
There might be such a will, to only conclude the contract later in this case, but does not has to. There is no general rule, that employment contracts are normally in written form. Instead the employee has the right to get a written confirmation of the essentials of the contract in case of a non-written contract (Nachweisgesetz). Only for the public sector there exists a jurisdiction, that employment contracts are normally (and according to the collective agreement) in written form, with the consequences of section 154 § 2 BGB (Landesarbeitsgericht Köln, Urteil vom 05. Februar 1999 – 11 Sa 1025/98).
So it depends on the detailed circumstances of the case when exactly the employment contract is concluded.
If it is concluded orally the employer has to write down the essentials, sign it and hand it over to the employee within one month (Nachweisgesetz). The employee has not to sign anything. It may be practically good for both sides to record the contract in written form and void the oral agreements, but that depends.