What I remember from school (late 90s) is that Babbage was inspired by Jacquard’s punched cards to use then in his Engine, and either this, or Jacquard directly, inspired the same in Hollerith. I don’t recall it as there being a direct line in terms of “modified loom is general purpose computer) but it was certainly an important influence.
In hindsight it seems easy for some of us to make the connection, but, at the time, it must have been quite the breakthrough.
I'm not disputing the influence of jacquard machines in general, but there is big difference between "having influence on computing" and "is a computer".
It's an interesting question, where the boundaries of an innovation lie. If we take Jacquard's loom as an 'ordinateur' or information ordering machine, its 'computing' properties become more recognisable -- composite outputs and patterns derived from stringing together smaller bits (and strings) of information.
In hindsight it seems easy for some of us to make the connection, but, at the time, it must have been quite the breakthrough.