The ex-trader was arrested in April 2010 as he was on the verge of leaving the French bank to take up a new post with Tower Research Capital.
He is accused of printing off hundreds of pages of code as part of a scheme to duplicate the same HTF system in his next role.
Mr Agrawal has been charged with theft of trade secrets and could face up to ten years behind bars if found guilty.
US attorney Thomas Brown, prosecuting, said: âSamarth Agrawal was a thief, but wasn't an ordinary thief.â
"He didn't steal cash or gold or diamonds. He stole something much more valuable. He stole a powerful way to make millions of dollars in the stock market."
He compared the secrecy with which the French bank protected the HFT codes to the way in which âKFC guards its recipe for chickenâ.
The trial, which is taking place in Manhatten, is expected to last two weeks - Mr Agrawal denies the charges.
HFT has come under increasing scrutiny in the US, especially since the âflash crashâ in the markets on May 6th this year.
By Jim Ottewill