Many in Europe see the US as more of a risky bet after the last four years, especially with the Iran deal hurting many EU businesses for what they have decided are not good reasons.
Local businesses suffering due to an ally will drive (and probably already has driven) policy changes in the EU 26.
What did they think 12 years ago when Iran was part of the Axis of Evil? If trust takes a long time to build, there shouldn't have been any generated here.
Can you include specific examples of how popular EU opinion has driven policy? Typically the foreign policy of nations depends less on popular opinion than on geopolitical concerns. Your argument might be stronger if it focused on Trump's isolationist military and trade rhetoric, which both pose a much more significant threat to the current order in Europe and are a more substantial break from past USA policy than its attitude towards Iran.
The arenas in which Obama tried to ~actually use~ soft power, such as Syria and Ukraine, seem more like failures than successes.