Paulsen was born in Augustenborg and started his youth career in local clubs Midtals, Haderslev and Sønderborg. On 1 January 2007, he joined the youth ranks of SønderjyskE.
SønderjyskE
Paulsen made his debut in the Superliga during the 2009–10 season, coming on as a late sub in a 1–3 away loss against Nordsjælland on 25 April 2010 at age 19. In 2010–11, Paulsen played 21 games. His first start for SønderjyskE came on 14 August 2010, home at Haderslev Football Stadium, in a 1–3 loss against Odense. A week later, in a 2–0 win against Horsens, Paulsen provided his first assist in the Danish top tier. The following campaign, in 2011–12, Paulsen played 19 games under the reign of new manager Lars Søndergaard. He provided 3 assists during the season, and scored his first Superliga goal in a fixture against Aalborg on 23 May 2012. Paulsen scored in the 75th minute as SønderjyskE won 5–0. In 2012–13, Paulsen established himself as an important first team player. He appeared in 31 games, scoring 3 goals. During the upcoming two seasons, Paulsen developed his play dramatically and progressed to become a highly rated defender and midfielder in the Superliga. He was also assigned the role as vice captain at SønderjyskE. The club finished 10th, just above the relegation zone, in both 2013–14 and 2014–15. Paulsen played 32 games and scored 4 goals in both of the separate campaigns. Ahead of the 2015–16 season, Jakob Michelsen was appointed as the new manager of SønderjyskE. Paulsen played an integral part during his first months at the club, appearing in the 7 first fixtures of the campaign.
Esbjerg
On 31 August 2015, on the closing day of the international transfer window, Paulsen transferred to Esbjerg fB in the same league. Reports suggested a fee of 5 million Danish kroner, as Paulsen signed a four-year deal. He made his debut on 14 September 2015, home at Blue Water Arena, in a 4–2 win against Odense BK. Paulsen started out playing as a central defender, but in October the same year, Esbjerg appointed Jonas Dal as their new manager. He used Paulsen at different outfields position, mainly in either one of the offensive winger positions. Paulsen scored his first goal for EfB against domestic giants F.C. Copenhagen on 28 February 2016. He scored the equalizer as Esbjerg lost 2–1 on away turf. In total, Paulsen made 25 league appearances in the campaign, scoring three goals, whilst being an important member of the Esbjerg squad. During the upcoming season, in 2016–17, Paulsen continued to play at either flank during the reign of new manager Colin Todd. However, the results during the first half went against Esbjerg, that soon found themselves at the foot of the table. Paulsen was soon named as one of five players that could be deemed surplus to requirements at the club during the January transfer window, due to his reportedly high salary.
On 16 January 2017, Paulsen was sold to the Swedish club Hammarby IF in Allsvenskan. He signed a three-year deal with the Stockholm-based side, whilst reconnecting with his former manager from SønderjyskE, Jakob Michelsen. The fee was reported as being 1,6 million Danish kroner. On 9 April, he scored his first competitive goal for Hammarby, a late equalizer as Hammarby drew 1–1 against Kalmar FF on the second match day of Allsvenskan. On match day 6, Paulsen scored a brace as Hammarby defeated the newly promoted side AFC Eskilstuna in a 4–0 win. He scored another two goals as Hammarby won against IF Elfsborg on 24 July, with Paulsen deciding the result to 2-1. Paulsen played 29 league games, scoring 8 goals, throughout the season and was voted "Hammarby Player of the Year" for 2017. In August 2018, following a number of impressive performances in the central defender position, Paulsen attracted interest from AEK Athens. Hammarby reportedly turned down an offer of around 8,4 million Swedish kronor from the Superleague Greece club. He eventually played 29 league games, scoring 5 goals, as Hammarby finished 4th in the league. He was nominated for the prize Allsvenskan defender of the year, that eventually was awarded to Per Karlsson, and chosen one of the eleven best players of the 2018 season by Cmore Sports, Fotbollskanalen and Playmaker.
FC Ingolstadt
On 7 January 2019, Paulsen completed a transfer to FC Ingolstadt in the 2. Bundesliga for an undisclosed fee. He signed a -year contract with the German club.
Style of play
Paulsen prefers to play as a central defender. However, he has been known as a utility player throughout his whole career in Denmark, making appearances in almost every outfield position during his time with both SønderjyskE and Esbjerg. At Hammarby, Paulsen started out playing as a central offensive midfielder, before pairing up with compatriot Mads Fenger in the central defence during the second half of the 2017 season.
