The 20-year-old continued his recent hot streak as he fired his 10th goal in 14 games to send Italy ahead on 35 minutes.
Balotelli provided a lay-off earlier in the move and the duo had also earlier combined before the Manchester City man cracked a shot against the crossbar.
While France battled back to snatch the win, thanks to goals from Mathieu Valbuena and substitute Bafetimbi Gomis, the partnership of Balotelli and El Shaarawy was a major plus point in a 4-3-3 that also included Antonio Candreva.
"Mario is a great player who can also provide goal scoring chances," El Shaarawy told reporters after the match.
"I hope we can be the pairing of the future. I am going through a good period right now and I hope it continues.
"It was an important goal for me, though sadly it was not enough to get a result tonight. We played a strong team so on a personal level I am very satisfied."
Azzurri boss Cesare Prandelli elevated a number of his Under-21 players for last night's match in Parma with midfielder Marco Verratti handed a start while Alessandro Florenzi made his debut.
"All these young players are capable of playing in games like this," El Shaarawy said.
"You can see that because they are doing well for their clubs and even the senior Italy squad should focus on youth."
Prandelli was happy with the way his young charges handled the shift to a new formation and believes the experimentation would stand his side in good stead for the future.
"We didn't deserve to lose this, but it was right to experiment and we will experiment again," he said.
"We need to be ready for tournaments and that means using these games to test things out.
"We did some good things, it was the first time we were trying the 4-3-3, so some movements were not going to be solid."
The 55-year-old, who took Italy to the Euro 2012 final in the summer, also praised the performance of this front men, adding: "The strikers did well and have different characteristics. El Shaarawy is very aware. I saw a good Italy side.
"If I had a few more friendlies and training sessions then we could see Andrea Pirlo and Verratti together, but for the moment we have to focus on qualifying (for the World Cup).
"It has been a great year."