The simple answer is yes, choose a .com top level domain. Country code top level domains are interpreted by Google in a way that tells them this is where your business or organization exists. If you purchase a .fr or .ly domain, Google will think that you operate out of France or Libya. This puts you in a bad position for SEO. If your top level domain is .fr, you will have a better chance of ranking in Google.fr than Google.com.
Try and avoid the trendy domain name extensions. We are all familiar with the .ly, .io, .me and all the other trendy domain exertions, but know that you are going to hurt your business as it relates to organic search. There are several cases such as Visual.ly where they rank for everything related to their business, but they DA is over 85 and have a huge online presence, that a small business just simply cannot achieve, so if you go this route you need to know that you have an uphill battle ahead. SEO can be hard enough, so it makes no sense to make it even harder by trying to convince Google that you are not in France and actually in the US.
Another item to consider is how your users will interpret the domain. Users in America are very familiar with .com, but not familiar with .ly or .io extensions. This may cause your users to forget the domain name, enter it incorrectly and you never want to put your user in a position where they cannot get access to the website.
Since we are on the topic of domain names, I am going to take this opportunity to rant. Stop buying keyword dense domains, just stop it. Yes, we know that they can still outrank non keyword dense domains. However, its not a good long-term plan, opens you up to over-optimization, future algorithm changes and diminishes your brand. So for those reasons, stop buying them.