Learn French: Nous n'aurions pas dû spéculer, la perte est grave. - We should not have speculated, the loss is serious.

To express "should have" (or "should not have") done something, French uses the past conditional of the verb devoir (to have to / must). You conjugate the helper verb avoir in the conditional (nous aurions), add the past participle of devoir (dû), and follow it with the infinitive of the action verb (spéculer).

Why are the negative words n' and pas placed around aurions instead of the whole verb phrase?

In compound tenses like the past conditional, the negation always hugs the conjugated helper verb. Here, that helper verb is aurions. The n' and pas go immediately before and after it, leaving the past participle (dû) and the infinitive (spéculer) outside the negative sandwich.

Why does dû have a circumflex accent (^) on the u?

The masculine singular past participle of devoir is spelled dû to distinguish it from the article du (meaning "some" or "of the"). It actually loses this accent in its other forms, like the feminine (due) or plural (dus / dues), because there is no longer a risk of mixing them up with other words.

Is grave the best word for "serious" here?