Your question is not clear. Is this a planting bed you are anticipating creating? Or just an edging closely adjacent to the fence line (for ease of mowing/weed control)? If the latter then, yes, keep it straight.

If the former, it is best to design a planting bed with the plants you hope to include in mind. That way you will be assured that the bed is large enough to accommodate them once they establish and mature. And since plants do not look at all attractive or natural lined up in a straight row unless you are doing a formal hedge, a long fenceline bed will often have gentle fluctuation in width....ie., soft curves. Often, laying them out with the hose first is a good way to judge both the width of the bed and its shape/curves before committing and digging.

Just don't get too squirrelly with too many indentations :-) Soft curves....gentle arcs.

A photo will help explain as well. Is there already a garden there? Do you plan to keep it as is, or will you be modifying the plantings? Regardless of answers to any of the questions above, test it out with you lawn mower before installing so that you can mow the edge without have to do any backing in and out of narrow areas.

Curves usually look better if they are long, sweeping curves that fit the surroundings. This is much better than waves or "bumps." Usually, curves will be combined with straight lines. Exactly how would depend upon what you are working with (the elements in your yard.) Photos that show overall spaces are helpful, but even more helpful is a base plan (a to-scale map of your yard showing the basic existing elements.)