I LOVED how the ministers dumped the talented detective before the killer was caught. Apparently they couldn't deal with a cop who knows how to get things done (tap all their phone lines.)
Die-Hard era Bruce Willis would never have quietly walked away if he'd been cast as the detective. If the Jackal was willing to continue the plot after being burned, John McClane would have pursued him no matter what!
Why are you comparing this classic with Die Hard. This is 1963 Paris. Lebel used uncanny detective skills way more cerebral and tasks way more time-consuming.
In the Jackal movie, they dumped Lebel because they thought they had enough info on the suspect and that the mole was revealed. That Lebel got them to a place where they could now get the Jackal within the two days was sufficient they thought. It had nothing to do with tapping of the lines. I am pretty sure getting the mole was the more important event for the preservation of France even though their private lives might not be so private.