Much has been talked about these past few days about Djokovic potentially missing events due to his unvaccinated status but that won't be a problem at the French Open.
The information was confirmed by French Sports Minister Roxane Maracineanu who responded to a question regarding the subject by saying:
"He would not follow the same organisational arrangements as those who are vaccinated. But he will nonetheless be able to compete [at Roland Garros] because the protocols, the health bubble, allows it."
Ultimately it means that Djokovic would be subjected to some sort of restrictions as an unvaccinated player in accordance with the guidelines and protocols established but he would be allowed to participate at the event nonetheless. It's a similar position to that of Wimbledon who also claimed they won't enforce a vaccine rule for the event.
When it comes to the US Open, nobody publicly said anything so there is a possibility they might enforce a vaccine mandate especially with the pro-vaccine stance of the US Government. The road towards that event is long and everyone hopes that the situation with the pandemic will be much better than before.