Good to know

Before leaving
http://biotoile.ujf-grenoble.fr
The Toile des Biologistes defines itself as "the network of Francophone researchers in life sciences." This association publishes the absolute must-have: "Guide to postdocs abroad" (downloadable).

https://erudera.com/study-programs/phd-degree/united-states/
Postdoc offers that you can select by discipline and by geographic area with an information sheet on the job offer.

http://www.fulbright-France.org 
Mobility grants.

http://immig-chicago.com/index.php?submenu=professional&ampsrc=gendocs&ref=2m_Visas_for_Science_and_Medical_Personnel&category=Professional-Skilled-Workers 
Information on immigration visas for researchers

http://www.payscale.com/research/US/Job=Postdoctoral_Research_Associate/Salary 
Average postdoc salaries in the US by large cities.

http://grants.nih.gov/grants/oer.htm
NB: a mailing list.

http://www.protocol-online.org

Coming back
http://France-science.org 
The science and technology mission of the French embassy in the United States announces recruitment fairs that are held in the United States in Boston for the "MIT European Career Fair" and in San Francisco for the " International Career Fair." Also note the "Young Entrepreneurs Initiative" to encourage companies start ups upon return to France.

http://www.biospace.com

http://www.biotechnologiefrance.org
421 are listed.

http://www.aipef.com

http://www.emploi.leem.org

Networks
http://frenchpostdoc.free.fr
A list of job websites.

http://www.biodocs.net
The Biodocs website (Association of young researchers in biology)