Although born in New York City, Coler was native to Newark, New Jersey. His parents were William Nichols and Lillie Seeley Coler, and his brother was William Nichols Coler III. Eugene Coler joined the RFC in Canada in 1917. After several weeks training, he embarked for England on 29 October 1917. He received further flight training in England. On 12 March 1918, he was assigned to No. 11 Squadron RFC, which was operating from Vert Galandon the Western Front. At that time, No. 11 Squadron was flying long range reconnaissance sorties.
Flying Bristol F.2 Fighter No. C792, he and his gunner Cyril Gladman attacked a formation of 14 German fighters on 9 May 1918. They drove three German Pfalz D.III fighters down out of control on this single combat sortie. On 13 August 1918, Coler and Gladman destroyed three Fokker D.VIIs and drove down two others out of control within a few minutes; Seeley won the DFC for this mission. The action began when Coler dived on 20 Fokker D.VIIs, setting one with a red nose and yellow fuselage on fire from a range of ten yards. He sent another spinning down out of control before his Vickers machine guns jammed. While he was clearing the jam, Gladman knocked a Fokker down out of control. As Coler cleared his guns' stoppage, a Fokker crossed before him 50 yards out; Coler fired 60 rounds into it and set it afire. Gladman then was shot in the right shoulder while changing ammunition drums. Nothing daunted, he shot it down left-handed, sending it down in flames. The following day, Coler and Gladman were forced to land behind British lines, the gunner being severely wounded. Their conqueror seems to have been Otto Könnecke. On 30 August, Coler changed gunners and planes, flying Bristol F.2 Fighter No. E2215 when he destroyed a Pfalz D.XII and a Fokker D.VII almost simultaneously. He then destroyed two enemy fighter planes each on 6 September, 15 September, and 16 September. On the latter date, he was wounded in action. Bruno Loerzer scored his 40th victory by puncturing the fuel tank and cutting the aileron controls on Coler's Bristol and driving it into a crash-landing near Beugny. While Coler was power diving into this controlled crash, two Germans who were chasing him overran their prospective target and were shot down by Coler and his gunner.
Bold in attack and skilful in manoeuvre, this officer never hesitates to engage the enemy regardless of disparity in numbers. On 13 August when on escort duty, he dived on a formation of twenty enemy aeroplanes. In the engagement that ensued he himself destroyed three and his observer two making a total of five machines destroyed in the fight; a fine performance, reflecting great credit on the officers concerned.