As answered to the question Is it possible to travel to Israel if it's not recognised by your passport's country? Israel allows citizens of all countries to enter its borders, as long as they have an appropriate visa. There are countries for whose citizens Israel doesn't require a visa for a tourist stay of no more than 90 days. Pakistan specifically doesn't recognize Israel and doesn't have diplomatic relations with Israel and is not on that list so a Pakistani citizen would need to acquire a visa prior to their visit to Israel.
For a european citizen the procedure is the same, even if they are a citizen of non exempt country, like Pakistan, as well, if they are from a country that is on the list then they can travel to Israel without a visa for a period of up to 90 days for tourism purposes. If they are from a country that requires a visa, then they need to acquire a visa before their visit.
If you plan to visit Israel with the Pakistani passport, you best contact an Israeli embassy and ask them about the needed procedure to acquire a visa, also, you would probably want to make sure that the visa will not be put inside your passport, as it may lead to problems with Pakistani authorities.And as noted in answers to other questions on this site, Israeli border control doesn't stamp a visitor's passport. This permits the the passport to have no record of the visit to Israel.
The closest Israeli embassy to Pakistan is in India, but a visa can be acquired from any Israeli embassy around the world, no matter the residence of the person applying.
One last thing, Israel, like all other nations reserves the right to not admit citizens of other countries to its borders for various reasons, people who come from enemy states, or states with no diplomatic relations, like Pakistan, are obviously more suspicious to Israeli security agencies, if you come to Israel using your European (or other friendly state) passport and are asked by the authorities about other citizenship, it's best to tell the truth and be forthcoming, trying to hide such information may lead to high suspicion and denial of entry.