Yet, it is important for progressives to have better control of the notion of freedom. So far, conservatives dominate the rhetorics on freedom.

I would make a distinction between factual  freedom (factual as in de facto), and nominal freedom.

Nominal freedom is the principle that you can do anything you want, within boundaries of law and established moral code. More precisely, you can anything you have power to do, within the boundaries of law and established moral code. This is the freedom that conservatives and libertarians mean. If you are in powerful position, you are indeed royally free. If you are in weak position, this is your problem.

Factual freedom is a venture of more opportunities for yourself and everyone. Say, you don't want to be very much dependent of illness, nature disasters, or other stucks of luck. These risks can be diminished across a society by means universal health care, education, etc.  Social agreements can make life more free in a sence that people may feel more secure, or have more diverse options to pursue their goals.

The problem witht he nominal freedom is the caveat "within boundaries fo law and established moral code". Why there are those boundaries? Why are there restrictions on the "freedoms" to taking things that you can easily physically reach (but they belong to others), or eliminate hurdles (by just murdering someone on your way)? Is not because societies without these boundaries do not have a logical chance to succeed? But "established boundaries" do evolve with time. For example, slavery was compatible with nominal freedom at one time. Who knows, soon enough we might need to update moral imperatives to respect not only citizen property and rights, but also natural needs of the Nature in order just to survive on this planet. The freedom to abuse your power has to be restricted in principle - we already have proper restrictions on physical power, but a successful civilisation may need to restrict economic and consumative powers as well.

On the other hand, the progressive "factual" freedom has still to win more appeal. It has to show that social contracts do make everyone more happy. Social contracts do cost more (freedom is not free, yeah!), or they force you to refrain from an immediate benefit. The problem is to show that everyone can win much more compared with tax contributions or missed immediate convenience. Social contract do work. For example, traffic rules do restrict your freedom to drive wherever or however you may wish - bu without traffic rules the would not be any traffic to satisfy our massive trasportation needs!