In ordinary news articles and such, 縁 is read as えん. When it's read as えん, it can refer to both a fateful/spiritual connection and a casual one. For example, 今��は縁がなかった ("We just didn't have en this time") is a common way of declining a business offer.
On the other hand, it can also be read as えにし. In this case, it more strongly implies a deep, often fated bond, typically between a man and a woman. But えにし is primarily used in poetic or lyrical contexts and is not common in everyday speech. If your sentence appeared in the oral storytelling of an old woman in a mystery game, reading it as えにし would feel equally natural.
If you're unsure which to use, remember to use えん first when you want to express the idea of a connection between people.
EDIT: @Arfrever pointed out that 縁 can also be read as ゆかり and よすが, and asked if these readings can be used in the given context.
- ゆかり is almost always written in kana. While it means "connection" in a broad sense, it is used almost exclusively in contexts involving historical or famous figures. In modern usage, it rarely carries religious or spiritual nuance. For example, it is used like "ビートルズゆかりの地 (a place associated with The Beatles)" or "ゆかりのある岩 (a rock with a historical story)". えん and えにし can be established by someone's will (including divine will, as in 縁結び), but ゆかり is not something formed by anyone's intention. While ゆかり is a valid reading of 縁 in girls' names, you generally don't have to consider this reading in ordinary written texts.
- よすが is also almost always written in kana, and means something one relies on psychologically or spiritually (i.e., a crutch). It is completely out of place in this context. I personally wasn't even aware that 縁 could be read as よすが in any context.
Practically, when there's no furigana, 縁 is read either as えん or ふち (as in an edge or border).
