A lot depends on what you mean by 'invasive'. All willows (Salix spp.) have aggressive roots, tree forms much more so than the shrub forms. Tree willows can grow to a very large size (60'+) and tend to have very aggressive, water seeking roots. They will invade any nearby water source (inground plumbing, water pipes/mains, irrigation systems, septic fields, etc. They are NOT recommended for a typical suburban garden.

In general, shrub willows do not have aggressive root systems and will not invade or aggressively seek out water sources. However, if they have been grafted and sold as a tree form, the grafted rootstock may very well have a more aggressively spreading root system than just the straight shrub. Keep in mind that the grafted form of dappled willow is intended for use in the average garden so unlikely to have the same overly aggressive, invasive behavior as would a weeping willow, for example.

How close will the hedge be in relation to the French drain?

These are not grafted and purely shrub form. I’d say they’ll roughly be planted 3’ from the trench for the drain.

3' is probably too close. The roots are very likely to encroach into the French drain.

Is there anything less invasive for privacy (evergreen or deciduous) you can think of that would work? I’m maybe thinking about putting a wider edging to prevent roots from encroaching. So something with more of a surface root?

One of my other considerations is Allegheny viburnum.

You run the risk of root encroachment with any shrub of size. Root spread will be equal to or exceed the spread of the shrub, unpruned.

A root barrier could be advised.

What’s the recommended distance to plant from it then? Like 6’?

How would the tricolor dappled willows do in a patio container? Just curious.