France visibly grew in confidence as the interval approached and both Hart and Ashley Cole combined to block Benzema as he closed in on the angle.
Benzema once again demonstrated his danger with a powerful drive that was saved by Hart - but this came in the middle of cagey, attritional exchanges.
Glen Johnson was also forced into a timely penalty area interception as Benzema threatened once more.
Hodgson made a double change with 13 minutes left when he sent on Jermain Defoe for Oxlade-Chamberlain and Jordan Henderson for the visibly tiring Scott Parker.
Hodgson's side continued to show resilience to get the reward for a dogged display - and they can look forward to taking the next step in Euro 2012 against Sweden.