This post aims to show as many Top 14 jerseys as possible for the upcoming season - after all, since it is also reasonably likely to be cancelled, those might become collector items in the future. And for those who care about it, I have been trying to identify both the brands, sponsors (and what kinds of companies they are) along with other anecdotes when I can find some.
The reason is that some sponsors really make the shirts uglier - I'm thinking of Bordeaux' Bourse de L'Immobilier on the chest, this one I'm sure will be more popular without sponsors. It's also interesting to see what kinds of companies sponsor rugby teams in France.
I'll try to update it when new kits are revealed (including Away/Third when applicable - although I will just link because the max number of images is reached there) - looking at you Stade Français. Also some sponsors are still missing due to me not having had access to all full kits yet, I'll see if I have the courage to look at butts in scrums to complete the list.
Image size has nothing to do with personal preference, I just tried to save some of my sanity by cropping the ones that were easier to crop (e.g. La Rochelle & Toulon). you can click on them I guess.
Favorite ones: Bayonne A, Montpellier H, Brive A
Edit: BTW, when I wrote "back - bottom" in the sponsor description, it means "bottom of the shirt, in the back", not "on the player's bottom" - that one is marked "shorts - back".

Agen

L & 3rd: Home, R & 2nd: Away
Brand: Errea
Main sponsor: Bigard (meat processing)
Other sponsors:

Mazda (automaker), chest - right
Accès Industrie (handling equipment rental), chest - left
UPSA (pharmaceuticals), back - top
Ultra Premium Direct (pet food), back - bottom
Saur (water and leisure management), left sleeve
Stef (controlled temperature transport), right thigh
Clima Froid Aquitaine (air conditioners and refrigeration systems), left thigh
Vigipets.fr (lost pet tracking service), shorts - back

Bonus: Video reveal of the new shirts. Apparently, the third jersey for European duties will be red, but it has not been revealed yet.

Bayonne

L: Home, R: Away
Brand: Kappa
Main sponsor: MGP (insurance)
Other sponsors:

Lauak (aeronautics contract manufacturer), chest - left
City of Bayonne (self explanatory), chest - right
Mercedes (automaker), right thigh
Maison Rivière (cooked meals), left thigh
Banque Française Mutualiste (Bank), back - top

Bonus: the motif on the Away kit is the Lauburu, or "Basque cross".

Bordeaux

Home

Away
Brand: Kappa
Main Sponsor: Arkea (insurance)
Other sponsors:

Bourse de l'immobilier (real estate), chest - left
Cdiscount (online sales), chest - right
Cacolac (cocoa drink), left sleeve
Fayat (construction), back - top
edenauto (car sales), back - bottom

Bonus: The V motif on the Home shirt is named a "scapulaire", and is a symbol of Bordeaux sports teams - the football team also usually uses it.

Brive

Home

Away

Third
Brand: Adidas
Main Sponsor: Vivendi (media)
Other sponsors:

Allianz (insurance), chest - left
De Richebourg (recycling and maintenance services), chest - right
Renault (automaker), left sleeve

Bonus: Vivendi is also the owner of Canal+, which is the Top 14's broadcaster.

Castres

L: Third, C: Home, R: Away
Brand: Kappa
Main Sponsor: Matmut (insurance)
Other sponsors:

Tarn (tourism agency from the region where Castres is hidden), chest - left
Sud de France (wine label), chest - right
Renault (automaker), left sleeve
Pierre Fabre (pharmaceuticals), back - top
Bigard (meat processing), back - bottom and right thigh
CCL (construction), shorts - back

Bonus: Video reveal of the new shirts.

Clermont

L: Away, C: Home, R: Third
Brand: Macron
Main Sponsor: Paprec (paper recycling)
Other sponsors:

Groupama (insurance), chest - left*
Omerin (cable manufacturers), chest - right
Renault (automaker), left sleeve
Michelin (tire manufacturer), back - top
Accenture (professional services), back - bottom
CGI (IT consulting), left thigh
Crédit agricole (bank), right thigh
Labo France (construction products), shorts - back

Bonus: Video reveal, but without players getting involved

La Rochelle

L: Home, C: Away, R: Third
Brand: Hungaria
Main Sponsor: Apivia (insurance)
Other sponsors:

Sodebo (cooked meals), chest - left
Merling (coffee roasting), chest - right
Avia Picoty (filling stations), left & right sleeves
Lea Nature (organic products), back - top
COGEP (accountants), shorts - back
Bigard (meat processing), back - bottom & right thigh
Charente Maritime (La Rochelle's county), left thigh

Bonus: It is the same shirt as last year - the Stade Rochelais decided to cut costs due to the uncertainty of the pandemic (they are the team whose stadium has the highest filling rate in the league and rely on it for their finances, hence why Covid hurts them a lot. Merling is the company founded and owned by La Rochelle's president, Vincent Merling.

Lyon

Home
Brand: Macron
Main Sponsor: Matmut (insurance)
Other sponsors:

6e sens immobilier (real estate), chest - left
GL Events (events), chest - right
Serfin (financial services), left sleeve
Eiffage (construction), back - top
BFM Lyon (media), back - bottom left
Justin Bridou (delicatessen), back - bottom right
EM2C (real estate), left thigh
Crédit Agricole (bank), right thigh
Samsic (business services), shorts - back

Bonus: Matmut is also the brand of Lyon's Gerland stadium.

Montpellier

https://preview.redd.it/qih7dvvi6kl51.jpg?width=1600&format=pjpg&auto=webp&s=c72184b1b2000f5fbec31d96950fe498efcdfecc

https://preview.redd.it/tw5nfvxj6kl51.jpg?width=1600&format=pjpg&auto=webp&s=69dfd0fcf508a7e933abc5570e91bff2f0e2cd41
Brand: Kappa
Main Sponsor: Altrad (construction equipment)
Other sponsors:

Hectare (real estate), chest - left
Montpellier métropole (self explanatory), chest - right
Hérault (Montpellier's county), left sleeve
Tressol Chabrier (car sales), back - top
Sud de France (local food producers), back - bottom
Urbaser (environment services), shorts - back
Crédit Agricole (bank), right thigh

Bonus: Altrad, whose founder Mohed Altrad is Montpellier's owner, is also the French NT's shirt sponsor.

Pau

L: Home, R: Away
Brand: Macron
Main Sponsor: Total (oil and gas) - also on the back of the shirt
Other sponsors:

Terega (gas transportation), chest - left
Cancé (metallic construction), chest - right
Autaa (handling and logistics), left sleeve
essor (real estate, shorts - back
Leclerc (supermarkets), left thigh
PLH (real estate), right thigh

Bonus: The twin peaks on the back of the shirt symbolize the Pic du Midi d'Ossau, the most famous summit in the Pyrénées-Atlantique county, with a height of 2884m, and whose nickname in Béarn is "Jean-Pierre".

Racing

Home

Away
Brand: Le Coq Sportif
Main Sponsor: Natixis (bank) - also on the back of the shirt
Other sponsors:

Clarins (cosmetics), chest
Assystem (engineering), chest - left
Hauts-de-Seine (club's county), left sleeve
alila (real estate), back - bottom
Foncia (real estate), right thigh
Andros (fruit and milk transformation), left thigh
Triangle Interim (temp agency), shorts - back

Bonus: Le Coq Sportif is also the brand used by the French NT.

Stade Français

https://preview.redd.it/sic5sto1tpl51.jpg?width=4096&format=pjpg&auto=webp&s=1ce377cabdebba07c9195942292d4ec3be620e25
Brand: Kappa
Main Sponsor: Capri-Sun (fruit beverage)
Other sponsors:

Talan (digital tech), chest - left
Acadomia (school help), chest - right

Bonus: What else but a list of 15 of the most emblematic Stade Français jerseys.

Toulon

L: Home, C: Away, R: Third
Brand: Hungaria
Main Sponsor: SPVIE (insurance)
Other sponsors:

Groupe Loudane (specialized transportation), chest - left
AGV Garelli (real estate), chest - right
Team Interim (temp agency), left sleeve
Volkswagen (automaker), back - top
Pizzorno (environment), back - bottom
yack (air conditioners), shorts - back
JOA (casinos), shorts - left thigh

Bonus: Shirt reveal video. The man in their back is Felix Mayol, whom you might know from the stadium's name - he was a singer in the beginning of the 20th century and a RCT fan, and funded the building of the stadium.

Toulouse

Home

Away
Brand: Nike
Main Sponsor: Peugeot (automaker)
Other sponsors:

Airbus (plane manufacturer), chest - right
Jimenez (logistics), left sleeve
Fiducial (accounting), back - top
Parera (cartography), back - bottom

Bonus: The stripes are inspired by the 85-86 shirts - they won back-to-back titles in these years.

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Top 14 2020/2021 Jersey Guide