Paris 1 month flat rental? Recommendations for reputable landlords or companies?

Check Guest Apartment Services. I've rented from them and they're great. https://www.guestapartment.com/

Not sure what their availability is in the 12-14th

I rented from ParisAttitude for three months Sept-Nov 2021. My experience was mixed. The website indicated lots of apartments as available that weren't when I asked explicitly. I think they hope for long-term rentals (more like a year) so your one month request may not appeal as much. You'll just have to see.
The apartment was absolutely fine and the landlords were good, cooperative. We had a couple of minor problems (TV wouldn't work when we arrived, couldn't get the heat to come on) but they were dealt with.
Big issue was that Paris Attitude overcharged me for initial deposit and first month's rent. They eventually refunded me some money but I was never convinced it was the full amount. The calculations seemed inordinately complex so it was hard to tell. And I deal with pretty messy budgeting in my job.
I chose them because they were recommended by the Alliance Francaise and some other study abroad places, so I figured they must be at least reasonably professional.
I'm undecided what I'll do next time I need an apartment in Paris but most likely it won't be them.

Thank you.
For work reasons, I'm limited an arrs. that will be convenient.
And I agree that ParisAttitudes may be more trouble than they're worth. Found a few other similar complaint situations regarding $... It seems that if there's a problematic landlord, ParisAttitudes does do much to support the renter.

For those unaware, this new Mobility Lease is now in place for Paris.
https://parispropertygroup.com/blog/2019/game-changer-new-rental-option-for-visitors-to-paris-gives-relief-from-airbnb-crackdown/

For those unaware, this new Mobility Lease is now in place for Paris.

Mobility leases are only available to residents or to those with business in France. Tourists do not qualify for mobility leases.

Yes. Tourism doesn't qualify. But students, internships & business-related visits do.

Try morningcroissant.com

I’ve rented apts through ParisAttitude twice and was very happy with the service and the apts, both apts were nicer than i expected. I wouldn’t hesitate to use them again.

Stay away from ParisBestLodge (might have changed name) but still run by Thierry and listed on VRBO. Thierry and the apt were a nightmare.

You might want to look at Paris Autrement. I know that they have a lovely apartment near Picpus metro station though many of their properties are in Le Marais.

I have used Cobblestone Paris, https://cobblestoneparis.com, and Apartments du Louvre, https://www.apartmentsdulouvre.com. I'm hoping to visit Paris again next year and will use one of these agencies for my stay.

Enjoy your trip.