Definitely not true on all counts, you are letting your ideology cloud your objectivity. Some aspects of French society might be called "socialist" (health care for all, free education, decent minimum wage and generally better protection for workers and the unemployed than in the US), but it is still a country where there is little to no public ownership of the means of production, and no central planning. It is a land of private enterprise just like the USA!
France just had a hardcore capitalist president with Sarkozy for 5 years (succeeding Chirac who was from the same party), and even under Hollande, nothing has changed regarding the general system of government. Ultimately, there's not much room to maneuver system-wise in the EU anyway.
To get back on topic, just like in the US the French government gives incentives for innovation in various sectors, and in France, public research institutes (CNRS, INSERM, CIRAD, etc.) and public hospitals have indeed been at the forefront of many breakthroughs, some that have won Nobel prizes, again thanks to support from the government, not in spite of it.