The flight to Israel does not take so long. From Frankfurt, it is on a direct flight 4-4, 5 hours flight to Tel Aviv Ben Gurion.
In the low season, you get flight tickets from 250 euros for one round trip per person. For the open jaw flights, the prices start from 170 euros. Proper bargains can be made with a flexible start and end of the journey (around +/- two to three days).
In general, it is recommended to have a passport that has not been newly issued to avoid unpleasant questions when entering or leaving the country.