Both are grammatical.
"Will" is followed by the basic form ("infinitive") of almost any verb (the only exceptions I can think of are modals like "can", "may", "should", none of which has an infinitive).
"Resume" is one of a large class of English verbs which can be used both transitively (of the person causing or initiating a process), and intransitively (of the thing undergoing the process). They are sometimes called ergative verbs.
So The chair resumed the meeting and The meeting resumed are both possible.
Other examples are "roll" (He rolled the trolley aside; The trolley rolled down the slope) and "start" (She started the car; the car started first time).
In the transitive sense, these verbs can be used in the passive, so The meeting was resumed by the chair.
So in your example, both the process will resume and the process will be resumed are grammatical and idiomatic. There is a slight difference in meaning, in that the process will resume suggests that it will happen automatically without anybody needing to do anything, whereas the process will be resumed suggests that somebody will make it happen; but these are only suggestions, and may not reflect a real difference in the objective events.