Dress code at L'Astrance
I have been there at least 5 times from no stars up to the present and have always worn a suit/tie or in cooler weather sometimes a sportcoat with a turtleneck sweater. This is an understated, elegant place, so why stick out and possibly make yourself uncomfortable by under-dressing? I have witnessed 2 men at lunch in only shirts and they weren't chastised, but my bias is to be respectful and dress appropriately.
Haven't been to L'Astrance but eaten at many other 3 stars. I always wore a good jacket, decent shirt (with collar), shoes (not sneakers), and never jeans. I have never worn a suit or tie and never felt out of place or underdressed. However, I always wore a suit and tie to work as this is still the norm in Paris offices.
I commented in another post that the way you dress is a sign of good manners and respect which are both essentials of French society. So if you dress well, even to go to the humblest cafe, you will probably get better service and enjoy the experience more.