Step 1: An open fracture means the fracture communicates with the outside through a skin breach, so the wound is contaminated by environmental flora and faces a substantial infection burden.
Step 2: Two viewpoints exist. The traditional teaching named the gram-positive skin coloniser Staphylococcus aureus as the top culprit. Newer hospital-based data, particularly for severely contaminated Gustilo grade III wounds, document a rise in gram-negative bacilli, and Pseudomonas aeruginosa is repeatedly named as the predominant organism in that updated picture.
Step 3: Sorting the distractors: Klebsiella, though gram-negative, does not top the list for open-fracture wounds; Gonococcus is linked to disseminated gonococcal septic arthritis and genital infection rather than traumatic wound sepsis; Staph aureus is the legacy answer but is superseded here by the gram-negative trend that the question targets.
Step 4: Aligning with the emphasised gram-negative shift, the chosen organism is Pseudomonas.
\[\boxed{\text{Pseudomonas}}\]