Since 2008, baobab-fruit dried pulp is listed as an ingredient on the European Union′s Novel Food Catalogue. By pulp production, 80% of the baobab fruit is discarded, forming side streams, namely, shell, fibrous filaments, and seeds. This study explored pulp and side-stream functional properties, including total dietary fiber (TDF), total antioxidant capacity (TAC), polyphenols, and water- (WHC) and oil-holding capacities (OHC), along with endocannabinoids (ECs) and N-acylethanolamines (NAEs) in pulp, seeds, and seed oil. Shell excelled in TDF (85%), followed by fibrous filaments (79%), and showed the highest soluble and direct TAC (72 ± 0.7 and 525 ± 1.0 µmol eq. Trolox/g, respectively). Pulp was the richest in polyphenols, followed by shell, fibrous filaments, and seeds. Quercetin predominated in shell (438.7 ± 2.5 µg/g); whereas epicatechin predominated in pulp (514 ± 5.7 µg/g), fibrous filaments (197.2 ± 0.1 µg/g), and seeds (120.1 ± 0.6 µg/g); followed by procyanidin B2 that accounted for 26–40% of total polyphenols in all the products. WHC and OHC ranged between 2–7 g H2O-Oil/g, with fibrous filaments showing the highest values. ECs were not found, whereas NAEs were abundant in seed oil (2408.7 ± 11.1 ng/g). Baobab shell and fibrous filaments are sources of polyphenols and antioxidant dietary fibers, which support their use as functional food ingredients.