The problem you'll face
Basically, it can be very tricky and sometimes disallowed, as several friends have found out unexpectedly in the past few years.
Let's take one example. He finished, left to Israel for a wedding, and flew back to spend a week in the UK, figured he'd enter on tourist visa (Kiwi, but also on working holiday visa). 7 hours later....he was told he had 2 days' special dispensation and not to come back any time soon.
So essentially, they told him that when you're in the UK on a Working Holiday - you have 2 years to have a 'Working HOLIDAY'. So the logic is you've had 2 years to see as much as you could want to see. There's no reason to come back in again on a tourist visa unless you're just trying to sneaky come back in to work under the table.
Which you and I know isn't always the case - we work until the end of our trip, have savings and now want to blow them on travel!! Sigh.
He eventually went up the chain 3 supervisors, each one wanting to deport him and blacklist his passport(!), until finally they gave him the dispensation.
I've had two others with similar but not as scary stories. Another had his work visa expire (he'd forgotten the date) so asked if he could just enter on tourist visa instead, and he was deported immediately back to Australia, with a black mark on his record for life as well.
Going to France will get your passport stamped, and at the very least, recorded on the computer, they know you're exiting and entering, but that's not the problem.
Now, presumably a lot of their problems stemmed from their lack of evidence they were going elsewhere. The first guy didn't have a flight, he had a planned trip to ride a motorcycle from London to Mongolia with me. So he couldn't really 'prove' he wasn't going back to work, aside from ringing up the company and getting them to say it.
The banned one didn't have a flight as he was fully intending on coming into the UK to work, he just thought his visa was valid.
The way to do it right
As visafirst explains:
Basically there is no fixed period that must be spent outside but I
would advise you to spend at least one day outside of the UK and enter
back once your working holiday visa has already expired on a visitor’s
permit. The time that you will be allowed to spend in the UK without a
visa depends on the passport you hold.
This is fairly sound advice, but misses the questions you'll raise returning. So any evidence you have that you resigned, have packed up, a final utility bill, and ideally your flight home as documentation, that would be good to have with you. But legally, as long as you can satisfy them you're not being an illegal weasel, then yes, you're totally fine doing what you're describing. Just expect some questions, and be prepared.