stay outside Paris ?

there's a condo/hotel called Royal Regency in Vincennes. lots of places near Disney Paris. It's a nice, somewhat holiday tourist area.

Ha, bad luck!
Nothing suitable at all in Paris? That would be better, overall.

This said, some suburbs right next to Paris are just as good as outlying Paris districts. Clockwise:
- Vincennes (+ nearby St Mandé, which is very tiny)
- Montrouge (excl. the area around Avenue Aristide Briand, which is a busy highway)
- Issy around Mairie d'Issy or Corentin Celton metro stops
- most of Boulogne (excl. the far south and the area around Pont de Sèvres metro)
- Neuilly (excl. avenue Charles de Gaulle, busy highway again)
- Levallois-Perret
Of those, Vincennes and Levallois would have my preference.

If those do not work, I would consider staying in Versailles: it is a town in its own right with a lot to see and do (both in town and in the vicinity), and the commute to Paris is pretty good, with several options.
Getting to Tremblay for the car rental would be a pain, however...

Would any of these work?

https://www.vrbo.com/en-ca/search/keywords:paris-france/arrival:2022-07-09/departure:2022-07-16/filter:17/@48.830269499460215,2.287624255468752,48.88843239848521,2.381008044531252,13z/minNightlyPrice/0/maxNightlyPrice/400/minTotalPrice/0/maxTotalPrice/3860?adultsCount=4&petIncluded=false&b1=120115185739&c1=uKIHz5RWPKB2RS6G1aSl-w&d1=509091300845&ds_aid=58700006941829899&ds_cid=71700000081699334&ds_kid=43700069875390147&ds_kids=p69875390147&filterByTotalPrice=true&gclid=CjwKCAjwk_WVBhBZEiwAUHQCmRJE29I8at9LKlon77HxrhDZj00RBYt1Da67yy0BSHiIf90bBe_7yxoClQsQAvD_BwE&gclsrc=aw.ds&h1=b&ha_t=::&k_clickid=CjwKCAjwk_WVBhBZEiwAUHQCmRJE29I8at9LKlon77HxrhDZj00RBYt1Da67yy0BSHiIf90bBe_7yxoClQsQAvD_BwE&klocf=9001335&ksdevice=c&ksprof_id=700000002190872&ktarget=kwd-298360407833&semdtl=a1=12607515536&sl=slp&ssr=true

If you do a search on this forum of Paris Vacation rentals you will find a few reputable agencies that rent apartments, the folks on this forum are very generous with giving wonderful referrals. You do not need to go through AirBNB exclusively.
You can also check Booking.com, as they have apartments and VRBO.com.
For that short of a stay I would stay as Paris central as possible to get the experience you are looking for and the time issue on getting the metro daily, between walking to the station, the transfers etc it can really eat into the day and add to travel fatigue.

Oh the “plumbing” excuse AKA “my apartment rental was illegal”

I’d suggest avoiding AirBnB in Paris just for that issue

Try Vacation In Paris. I’ve had good success there.

Here is an AirBNB for your dates, no washing machine but indicates Laundry close by:
https://www.airbnb.com/rooms/39154985?adults=3&children=1&location=Paris%2C%20France&check_in=2022-07-09&check_out=2022-07-16&federated_search_id=4a7ab75c-1bdc-48d2-a5bd-de237b6e5d3b&source_impression_id=p3_1656606712_zQ8Bs4eay4X8rFqt

And another, no mention of a washing machine, but that is just something I would personally work around and plan to do full laundry on my previous location just before PAris:

https://www.airbnb.com/rooms/35895182?adults=3&children=1&location=Paris%2C%20France&check_in=2022-07-09&check_out=2022-07-16&federated_search_id=4a7ab75c-1bdc-48d2-a5bd-de237b6e5d3b&source_impression_id=p3_1656606844_lNQGbx1E%2BmhgwKRY

Thanks for all those answers !

I know that the ''plumbing problem'' seems to be a common scam but that renting have a registration number (starting with 75) so perfectly legit.

Of course there's other lodging on airbnb and such but it's not the best ones at this time ! Many of your recommendations are full (Regency, vacation in Paris) .

Bastille Day is July 14 so the lack of accommodations could be partly from that. I agree with Balso’s idea of looking further out to Versailles and other suburban towns. You might also check availability on VRBO ( Vacation Rentals By Owner).
Good luck!

Have you tried splitting up the trip? You could spend a couple days in Reims for example and maybe the airbnb availability will be better for a shorter time?

also airbnb has this policy "In the unlikely event a Host needs to cancel your booking within 30 days of check-in, we’ll find you a similar or better home, or we’ll refund you."

If you only want an Airbnb for the washing machine, why not just go to a hotel with laundry services? Then you can be more central?

I’m sorry, but a 13 digit registration number starting with 75 means that the person who lists the unit knows how to write a registration number with 13 digits starting with the 75.

Airbnb does not check the validity the numbers and it’s pretty common knowledge that people are just making up numbers. Sorry but a registration number just means somebody knew how to write one

Unfortunately there’s no way for you or I to know if the registration number is valid or something someone made up.

Of course it’s also possible that the plumbing issue is “I can make more money because it’s a holiday week” That recently happened to Sarah of adventures with Sarah who used to be a tour guide with Rick. And all Airbnb did was give her money back. They sent her the list of places available that weren’t actually available and gave her a refund. It’s not really a very good guarantee. They don’t do anything to the owners besides put a blurb on the reviews saying “a reservation was canceled by the owner.”

Unfortunately, the registration number scheme only lets the potential renter know one thing for sure, the lack of one strongly indicates an illegal rental. The presence of a registration number only suggests legality. There is no way for a visitor to know definitively that the apartment which interests him is completely legal and has not exceeded its maximum 120 day, annual rental period.

This is not the first plumbing problem cancellation I have read about, there will be more. Owners, not agencies, renting short term apartments can be fined up to 50,000€, and it will take city inspectors some time to weed out all the bad players.

Thanks once again to everyone !

Just a quick upadte, the owner told me that the plumber came and couldn't find what happened but the problem is now gone. It could never come back or came bak the next day. Since the apparment ticks all our boxes we will keep it, The owner was very open and precise in her anseers and assure me of a full disponibility if something should happen during our stay.

She also told me to not worry that we will find a money arrangement if we have to leave the location during our stay. ''we wont leave you alone'' is the words she used (well something like that since we are communicating in fench !) .

Someone will occupy the appart for 5 days from today, som I guess we will know if something happen.

Well, that's encouraging!
"Plumbing problems" are often used as an excuse (as mentioned above), but genuine plumbing problems do happen very often in Paris... typically, I would not trust my apartment's plumbing enough to rent it short term!
Fingers crossed, then.