The EU was heavily involved in negotiating the deal, see here. Europe also has better relations with Iran than the US has with Iran, this means that the EU isn't likely to yield to the US on this issue unless there is convincing evidence that Iran is violating the terms of the deal.
While the current US administration is not happy with certain details in the deal, for the EU and the other signatories one important pillar of the deal was to get to an evidence based process where all issues would be dealt with in a pragmatic way. Iran agreed to limit its enrichment program, not simply because of a bargain involving the lifting of sanctions, but also because the deal recognizes that Iran does have the right to enrich uranium in the future should the need for that arise. Iran therefore has no need to secure that right over the objections of other countries, and can then agree not to enrich uranium as currently all their enriched uranium needs are going to be provided for by Russia.
What the US now wants to do is to return to the policy of the Bush Administration, i.e. no enrichment ever in Iran. The argument that the deal has sunset provisions that would allow Iran to produce nuclear weapons is seen as a straw man attack in Europe, so this is not taken to be a serious flaw of the deal. Rather the fact that Iran is going to be gradually rehabilitated as an NPT member, is seen as an essential part of the deal.
Abandoning the deal would also mean that demanding that Iran sticks to the JCPOA limits on its nuclear program would have no legal basis. Iran could then enrich uranium within the usual IAEA framework that countries like South Africa or Brazil also stick to. If the US and Israel were to consider taking strong measures against Iran then the EU would find itself in a difficult position. If the EU were to try to take a middle ground in this sort of a situation where the US is bullying Iran into complying with its demand, how can the EU then ask Putin to stop meddling in Ukraine with a straight face?