Answered by Sayyidi Habib Umar bin Hafiz (may Allah protect him and benefit us by him)
What is the best response to attacks upon the Prophet ﷺ like the French cartoons?
The best response is to educate people about the Prophet ﷺ through public talks, conferences and social media. The perpetrators wish to divert the Muslims from doing that which benefits them, so we should ignore them and show the falsehood of the cartoons without mentioning the cartoons and those who drew them. The fact that people pay attention to the cartoons helps them to spread.
We should look at how Allah responded to those who abused the Prophet ﷺ. Rather than directly reporting their words and mentioning their names, Allah asserts the greatness of the Prophet:
You are not, by the favour of your Lord, a madman. You shall have a reward that is unlimited. Yours is indeed a tremendous character.
So I swear by all that you can see and all that you cannot see that it is indeed the word of a Noble Messenger. It is not the word of a poet. Little do you believe. Nor is it the word of a soothsayer. Little do you remember. This is a message sent down from the Lord of the Worlds. 
This is our response and there is nothing better than the way Allah responds. If we respond to everything which they do in the way they want us to respond then we will lose our way. Many of us act as if we do not have an example to follow. So let us follow the teachings of Allah and His Messenger ﷺ and this will be a means of success and victory.
 Al-Qalam, 68:2-4
 Al-Haqqah, 69:38-43