Kurzawa was born in Fréjus, France.
He made his professional debut on 22 September 2010 in a Coupe de la Ligue third round match against Lens at the Stade Louis II.
He started the match and played 65 minutes before being substituted in a 1–0 victory.
Three days later he made his Ligue 1 debut, starting in a 1–2 defeat at Lorient.
Kurzawa played four more league matches, all of them starts, as the season ended with relegation to Ligue 2; he was sent off on 1 May 2011 in a 1–1 draw at Saint-Étienne.
He made four appearances as they returned to the top flight at the first attempt as champions.

Kurzawa established himself in the first team for the 2013–14 season, with 28 league appearances as Monaco finished runner-up to Paris Saint-Germain.
He also scored five goals, the first of his professional career confirming a 2–0 win at Guingamp on 14 December 2013.

He scored in each leg of Monaco's 7–1 aggregate win over Young Boys in the third qualifying round of the 2015–16 UEFA Champions League.
Kurzawa was born in Fréjus, France. He made his professional debut on 22 September 2010 in a Coupe de la Ligue third round match against Lens at the Stade Louis II. He started the match and played 65 minutes before being substituted in a 1–0 victory. Three days later he made his Ligue 1 debut, starting in a 1–2 defeat at Lorient. Kurzawa played four more league matches, all of them starts, as the season ended with relegation to Ligue 2; he was sent off on 1 May 2011 in a 1–1 draw at Saint-Étienne. He made four appearances as they returned to the top flight at the first attempt as champions.
Kurzawa established himself in the first team for the 2013–14 season, with 28 league appearances as Monaco finished runner-up to Paris Saint-Germain. He also scored five goals, the first of his professional career confirming a 2–0 win at Guingamp on 14 December 2013.
He scored in each leg of Monaco's 7–1 aggregate win over Young Boys in the third qualifying round of the 2015–16 UEFA Champions League.
Layvin Kurzawa