* Bank of France forecasts economy grew 0.1 pct in Q1
* Industry, services surveys flag weaker activity
* Trade balance worsens, deficit widest since mid 2012
PARIS, April 9 (Reuters) - France's central bank forecast on Tuesday that the euro zone's second-biggest economy narrowly averted a recession in the first quarter, though business and trade date painted a picture of a still struggling economy.
The Bank of France estimated that the 2-trillion-euro economy posted growth of 0.1 percent in the first three months of the year, unchanged from its previous call.
If confirmed by official data due in May, the figure would mean France sidestepped what would have been its third recession since the 2008-2009 financial crisis after contracting by 0.3 percent in the final quarter of 2012.
Nonetheless, the central bank's monthly business climate survey, which the forecast was based on, suggested the outlook for growth remains anaemic, with manufacturing and services companies reporting weaker activity in March.
The survey found industry sentiment slipped further away from its long-term average of 100 to 93 from 95 in February while its services sentiment index slipped to 88 from 89, hitting its lowest level since July 2009.
Companies are suffering from slumping domestic demand because consumers are cautious about spending with an unemployment rate to 10.6 percent, the highest in more than a decade.
Foreign demand is not picking up the slack.
Customs data published on Tuesday showed the trade deficit widened to 6 billion euros ($7.81 billion) in February, the widest gap between exports and imports since June 2012.
The trade deficit, one of the starkest symbols of France's declining international competitiveness, worsened as exports dropped 1.9 percent month-on-month and imports fell 0.8 percent.
President Francois Hollande's Socialist government has cut its 2013 growth forecast to about 0.1 percent from a previous target of 0.8 percent due to the gloomy outlook. Most private economists consider France will be lucky to post any growth at all this year.
The feeble growth rate, which has forced the government to abandon a pledge to cut the public deficit to 3 percent of output this year, is increasingly straining public finances.
Monthly budget data also published on Tuesday showed the deficit widened faster in February than a year ago as weak economic activity weighed on tax revenues.