|Apparently, the US Senate doesn't realize they're involved|
Setting aside for now the specific question of why it is only Iran, an NPT signatory in full compliance, that finds itself subject to these kinds of sanctions and demands, today I'm merely noting that the right wing ideologues, in the guise of the United States Senate, have effectively interfered with the American ability to conduct American foreign policy. This has large ramifications for the future of American governance, but in the case of the Iranian negotiations seems to utterly fail to notice that the US and Iran are far from being the only players involved.
You see, there are two kinds of sanctions. Sanctions imposed by UN Resolution, which are upheld by all UN member states by treaty obligation, and sanctions imposed unilaterally by a nation's government. The second kind are voluntary - there is no legal obligation for any other nation to implement them. The US has often compelled international support for unilateral sanctions by using her enormous global economic clout to further sanction any company or institution, even those in friendly nations, if they violate sanctions imposed solely by the US Congress. This is analagous to a man holding a crowd at bay with a revolver - nobody wants to be one of the six people he can shoot, but if the crowd is sufficiently motivated they will accept the cost and overwhelm the man when he runs out of bullets. In the same way, if the EU comes to perceive the US as the primary obstruction to a nuclear deal with Iran, they will simply bypass the US, forge an agreement with Tehran and eliminate the sanctions as long as Iran is compliant. The US might continue to impose unilateral sanctions, but they would be perceived as pointless punishment, while the rest of the world happily welcomed Iran back as a trading partner.
It is worth mentioning that France could be problematic in this scenario. They have, in recent years, chosen to align themselves quite closely with Saudi Arabia, and are therefore quite hawkish on Iran, both on the nuclear issue and in more general terms. If the negotiating bloc fragments too thoroughly, the agreements will not be strong enough to change the status quo. But France has much closer ties to the UK and Germany than the US, so it would be surprising if they ultimately blew up a deal.
There is a point where America's inability to govern itself effectively will have a powerful impact on her broader place in the world. If the US Senate wants to suggest that they could unilaterally break an agreement signed by seven nations, those nations will feel they have no choice but recognize that constitutes a rogue, pariah nation that cannot be trusted to live up to its most basic agreements. And when the US congress itself denies the legitimacy of the US President, that President's credibility and authority is weakened all around the globe. The damage that America's radical shift to the extreme right has already done, economically, socially and politically is profound. As the partisan ideological divide becomes deeper and more acrimonious, the wreckage will continue to pile up.