You can use the SD.remove(filename); command from the SD library to remove a file from your SD card connected to your Arduino. The function must be called from your program running in SRAM on your microcontroller.
//client.println("<input type=button OnClick=SD.remove(entry.name())> cliquez pour supprimer</>");
Unless you have a javascript function called SD.remove(filename) that communicates with your microcontroller to likewise call SD.remove(filename) from Arduino's SD library you cannot use the above method to do this.
When a computer connects to an HTTP server that computer's browser interprets the HTML and runs any javascript on the local computer and displays the webpage. It can only make requests from the HTTP server. You would need to make a request from the server at an endpoint. Then have the server's endpoint handle the request.
Your server running on your Arduino (that also has the SD card connected to it) then can handle the delete by calling SD.remove(filename).