So, just to get on the same page, you have a .fr ccTLD but you want to target US, UK, Middle East, etc. Is that right?
Remember that a ccTLD is a hint to Google that it is targeted towards that geographical region. But, at the end of the day, a TLD is a TLD. What makes a site rank for a given term is far beyond just the TLD. Do you have different pages in different languages? Is that copy well written in those languages or are you simply dumping them into a translation program? Do you have links from the regions you want to target?
There's no reason a .fr can't rank well for any term in any region. I see .co.uk results in the US SERPs all the time. But it does bring up another problem: user behavior. If a UK person sees a .fr they might skip your site, assuming it's French. Then again, they might just ignore the ccTLD and click it anyways. it might be best to get a gTLD instead if you want to go the single site route.
The best solution with geotargeting is always to segment by ccTLD. There's no duplicate content penalties, each domain sends its own hint, and it makes marketing it all easier. Plus users know that domain is for their country/region.
As for Google+... depends on your answer to the question above. If you're going to segment by ccTLD then build a localized page. if not, go with a company.