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A) If you use a .com and it does well in google.com use a .fr host for the site to do well in google.fr for Pages : France
B) The serps at google.com were nearly an exact mirror of the web option serps in the regional googles
I have found during the last week for keywords/phrases in English that go to pages in English:
A .com, hosted in the US, is not in the first 1000 results in Google.com or Google.ie when using the Web option yet is number one in Google.ie when using the from Ireland Option.
A .co.uk, hosted in the UK is not in the top 10 pages of google.com or google.co.uk but is 1st page in Google.fr
A com site with no french content, hosted in the uk, came nowhere in the serps of google.com or .co.uk yet was position 4 on the front page for pages:france in google.fr and had not one backlink from a .fr site
Two com sites hosted in the US that are 1 and 2 in google.com change rank position when using the "web" search option in google.co.uk
A com, hosted in the UK , is position 5 on page one of google.com yet drops to position 9 on google.co.uk as co.uk domains hosted in the UK move above them.
A co.uk, hosted in the UK, that for over a year is seen on the 1st page of both com and .co.uk during a "dance" but is buried when rolled out as I guess a filter hits it. Whilst still buried on com it is now front page on co.uk
We found much the same across regional domains such as .de, .es, .sk, .se etc.
We found this across a range of sites with keywords and two and three key phrases that return from 70,000 to 2,000,000 results.