I will try right now to paint the picture (using current live rankings which may change) for women's doubles:
Automatically qualified, based on top 10:
(Mertens with whoever she chooses in top 300, it is impossible for Belgium to qualify another team otherwise)
(This one is complicated because Hsieh doesn't get along with the Chan sisters, so she will probably play with Wu, but L.Chan hasn't played since last year so if she has a protected ranking she can use it to enter with her sister, otherwise Hsieh can play with someone else and H.Chan will qualify by ranking with Wu so they have two teams but I think it is more likely to see Hsieh/Wu and then if L.Chan is retired or injured then they will only have one team in Paris)
(Routliffe can choose to play with Sun or Hourigan only, as they have no one else in top 300 and no chance to qualify a second team)
(Dabrowski with whoever she chooses, probably Fernandez. If she chooses someone like Marino then Andreescu/Fernandez can also qualify via ranking, but I think she will pick Fernandez so Canada will only have one team)
(This is another tricky situation because they can possibly get two teams depending on which combination they go with, but I think the likely one is Kerber/Siegemund which means the next highest ranked pair is Korpatsch/Maria and they would need a bunch of withdrawals to get in, now if Siegemund plays with Maria for example Kerber/Korpatsch will probably qualify)
(Zvonareva is top 10 and I don't know what pairings they will use but Russia will definitely qualify 2 teams)
(Hunter and Perez are top 10 but Hunter is injured-long term and will miss Paris, so the other AUS spot gets reallocated to the combined ranking route. Gadecki/Tomljanovic would probably qualify by ranking so if Hunter chooses someone else like Saville or Sharma, then AUS can have two teams. If she plays with Gadecki or Tomljanovic then chances are low for AUS to have a second team)
(Melichar is top 10 but like Russia they will have two teams regardless)
(Siniakova is top 10 but they will have two teams regardless)
So based on the above, we will definitely have these 12 teams:
With each potentially adding another team, so we'll say yes for now and that makes 15 teams
will all also have 2 teams by ranking, so now we're up to 21 and this is where things get complicated.
can all only have 1 team by ranking, probably Bucsa/Sorribes Tormo, Rus/Schuurs, Danilina/Rybakina, Azarenka/Sabalenka.
can have 2 teams by ranking, but only if Swiatek plays with Kawa or Piter, which I'm sure won't happen, so they will also probably have just 1 team which would be Swiatek with Frech or Linette. So that's 26 teams.
I think were aiming for 2 teams, with Stefani getting a top 10 spot to play with Pigossi who is outside the top 100 but they won bronze together in Tokyo, and Haddad Maia with Gamarra Martins who would also qualify by ranking. Now Stefani is 11 and withdrew from Roland Garros so can only have 1 team in Paris probably and probably Pigossi won't play, it'll be 2 of the other 3 girls. Only chance for Pigossi/Stefani is if there are a ton of withdrawals or if Pigossi wins a big 125k or something in singles next week and rises into the top 100, but as of now only 1 team for Brazil, so that's 27.
played with Boulter/Watson at Roland Garros so probably that will be their team for Paris. With other combinations they could possibly qualify a second team if they do Boulter/Nicholls and Lumsden/Watson but that still wouldn't be 100% certain so they'll likely stick with the 1 team, becoming the 28th team.
won't need to use their host spot as Garcia/Mladenovic will qualify anyways, and then Burel/Parry would be borderline, but if Gracheva wins her next match at Roland Garros then she would move up a lot in the rankings and Burel/Gracheva would definitely make the cut, but let's say for now France only has 1 team, so that's 29.
Based on their historical partnerships, I think we see Begu/Niculescu qualify and then Bogdan/Cristian are borderline. Cirstea hasn't played for the national team since 2018 so I don't think they could even make an exemption for her, and she didn't seem to care about missing Tokyo so I don't expect her to be in Paris either.
Errani/Paolini will qualify and Bronzetti/Cocciaretto are borderline. That is 31 teams.
Now for the last spot, based on the current live rankings:
Burel/Parry (106)
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Grammatikopoulou/Sakkari (108) - But Sakkari said she wants to play with Papamichail, but Papamichail/Sakkari would be 118 right now, so if they don't make it then I guess she will still try with Grammatikopoulou? I'm not sure.
Bronzetti/Cocciaretto (110)
Bogdan/Cristian (118)
Martic/Vekic (119)
Babos/Bondar (119)
Badosa/Bouzas Maneiro (120)
Ostapenko/Semenistaja (126) - I think Sevastova has a higher protected ranking that would get her in with Ostapenko but I think she has a bad injury and won't be able to make Paris. Not 100% sure though.
Frech/Kawa (128) - If the first team is Linette/Swiatek.
Olmos/Zarazua (129)
Pigossi/Stefani (130) - If Brazil chooses Gamarra Martins/Haddad Maia, otherwise Pigossi with one of the others would be even lower than 130.
Lumsden/Nicholls (131)
Mihalikova/Schmiedlova (134)
Of course also we don't know what will decide, but if they only have 1 team each then it's possible for more teams after Burel/Parry to get in.