A handful of people have reported this problem. At least in a couple cases quick and auto saves were ok, and it was manual saves that caused the problem.
At least in one case, the playtime in the default name (after the location) was not displayed properly, as if the characters were not supported.
The name should be of the form: A Nautiloid in Hell - 0h 12m
When you bring up the manual save option, is the playtime displayed properly? If not, does deleting the end of the name allow saves to be made properly, without affecting disabling saving/loading or preventing options from being selected in the in-game menu?
EDIT: before anyone checking out this topic for the first time tries troubleshooting, this issue is at least caused by a localisation problem with the French loca.
This should be fixed in a hotfix.
Are you shutting down all non-essential programs before starting the game, especially anti-virus and any backup programs, etc, that may be monitoring disk activity?
Try verifying local files: in the Steam library, right click on the game and select Properties, switch to the Local Files tab and then click on the 'Verify Integrity of Game Files...' button.
With the GOG version, in the (optional) Galaxy client, select the game, then the settings icon at the top right (beside the Play button) and under Manage Installation select 'Verify / Repair'.
Are you getting a data mismatch error in the launcher? If so, it would have created a log file listing any files in the install folder which are not expected, as well as files in the Mods folder. To check this, if applicable, copy the line below into the location bar in Explorer and hit Enter, then look for a text file named steam_4.1.1.2064610_alteredFiles.txt (or similarly, starting with 'galaxy_', for the GOG version).
%LocalAppData%\Larian Studios\Launcher\Cache
If applicable, disable Steam cloud support either globally (in the client click on the Steam menu and select Settings, and then Cloud) or just for this game (in the library right click BG3 and select Properties, then switch to the General tab and check the Steam Cloud section).
Alternately, exit out of the Steam client, or Galaxy for the GOG version, and just start the game directly from the executable when required.
Next, try browsing to the 'C:\Users\<UserName>\AppData\Local\Larian Studios' folder and rename the 'Baldur's Gate 3' subfolder. The easiest way to get there would be to copy the line below into the location bar in Explorer and hit Enter.
%LocalAppData%\Larian Studios
This folder contains the saved games, configuration files and a level cache folder. Deleting or renaming it will get the game to recreate it on startup; playing the game from a different Windows user account would effectively do the same thing. With Steam/Galaxy running and cloud support enabled, the client would just download the cloud copy of your existing profile.
Next, extract the replacement folder from
this download into your '..\Local\Larian Studios' folder, start the game and see if you can make a manual save successfully. If so, exit and copy a couple saves from the renamed folder into the newly created profile's ..\Savegames\Story folder. If that continues to let you start the game, load the saves and re-save, move the rest of the saves over.
The graphicSettings.lsx file is set to 1280x720 Windowed mode and Very Low quality preset, which you can change in the options (manually, or hit autodetect) if this gets the game working.
If you have the same problems after trying to save, you can delete the replacement BG3 folder and rename the original back again.
Try doing a clean boot and then test the game. Click Start, or hit WinKey-R, type in msconfig and hit enter; in the General tab, click Selective Startup, uncheck Load startup items (if required) and leave Load system services and Use original boot configuration options checked. Next, click on the Services tab, check the box to Hide all Microsoft services, then click the Disable All button (maybe make a note of which are currently enabled/disabled), then click OK and reboot the computer.
Run msconfig again to switch back to the normal boot configuration.
Try creating a new Windows administrator user account, switch to that account and try starting the game from there, directly from the executable to test.