I checked other news sources to verify if it was true. The BBC, which reported this claim, stated, "French officials say", therefore, I checked the French news source, Le Monde. Le Monde stated, "An Indian man died off the French coast on Sunday as he tried to cross the Channel." Man dies trying to cross the Channel, French authorities say
Additionaly, according to AP News, "An Indian man about 40 years old died on Sunday morning in northern France after the inflated boat he and other migrants had boarded to cross the English Channel deflated, French authorities said in a statement." It also states, "This was just one of many attempts by migrants to cross the channel since weather improved on Monday." indicating that this incident is not an isolated case but has happened multiple times before. Migrant man dies trying to cross the English Channel after small boat deflates | AP News
Therefore, this claim is not exaggerated.
Since both news reports are the same thing, this claim is an undisputed fact.