This is a rapidly changing situation and my personal experience might not be relevant in few days, saying that, this is what we have done:
We reached out to the France authority using the email at the bottom of the Passenger Locator Form, they eventually replied to it (6 days later), saying that if you are just passing through France you don't need to quarantine.
We left UK on the 27th of December using the euro-tunnel, we had to present: a negative tests, fill a passenger locator form (where we added our final destination in Italy and the compelling reason to travel) and we had to sign a swear declaration. We upload all the information in advance and we received a confirmation that our documents where in order few hours before departures. Only the test check takes time, the other two documents where confirmed immediately.
The compelling reason to travel is automatic if you hold a European passport (or your are a spouse of a passport holder) and you want to reach your native country.
We took the route passing through France, Belgium and Germany without any further check. We stopped overnight in Germany and we travel across Switzerland and cross the Italian border on the evening of the 28th.
The Switzerland government provide a web site where you can check your situation https://travelcheck.admin.ch/home
In our case, we didn't have to do anything in particular.
On the Italian border, in theory, you don't need any further tests or forms to fill, because the freedom of movement within the union, however, we cannot confirm that because nobody stopped us at the border to check.
The web site of the euro-tunnel gives you the options of the "compelling reasons to travel", however, I remember to be able to access to the full list of choices only after I purchased the ticket, during the upload of my data. I am not sure if this is an oversight on their side or it is deliberate.
In the end, the bought the full flexy options that allow full refund in case of cancellation and the capability to get to the first train available (probably an overkill, but it was indeed a smooth experience). I will recommend at least to buy the intermediate option that allow the full refund in case of cancellation.
Another option, probably a bit more time consuming is to book over the phone and double check with the operator if you have meeting the requirement of "compelling reason to travel".
It was my first time getting the euro-tunnel, so I cannot really compare it with anything, but the place looked not busy at all, I probably saw less then 10 cars in total during my checking, pet-scanning and embarkment process.