Fučíková started her career in the 1990s with illustrations for classic children's books, such as works by brothers Grimm, Hans Christian Andersen[3] or Oscar Wilde,[2] then changed her focus to stories about Czech history, citing her son's ongoing education as a source of motivation.[3] In 1998, one of her books was included in the IBBY Honour List.[2] She also won the first prize at the illustration biennale in Tehran.[2][3]
In the 2000s, Fučíková collaborated with the writer Alena Ježková [cs] on various publications concerning Czech history, such as books on Bohemian and Moravian legends or on Charles IV.[3] Her biggest undertaking in the field of history was illustrating five-hundred pages long Historie Evropy ("History of Europe") written by Daniela Krolupperová [cs] and published in 2011.[3] With the same author, Fučíková also prepared two history exercise books.[3] The illustrator also designed a variety of stamps for the Česká pošta.[2][3]
Fučíková won a number of prizes, including the Zlatá stuha [cs] (Golden Ribbon) awards for illustrations in a work on Tomáš Masaryk (2006) and in Příběhy českých knížat a králů (2007), and went on to win three more of these awards in the 2010s.[3] In 2011, Fučíková was nominated for the Astrid Lindgren Memorial Award.[3] Three years later, her Hus a Chelčický, a book for older children about Jan Hus and Petr Chelčický which she both wrote and illustrated, won the Association of Czech Graphic Artists HOLLAR award for illustrations.[5] Fučíková was also nominated three times for the Magnesia Litera awards.[6]
In 2016, Fučíková became the head of the Studio of Didactic Illustration at the Ladislav Sutnar Faculty of Design and Art of the University of West Bohemia.[4]
Fučíková is a member of the Czech section of IBBY and of Klub ilustrátorů.[2] She was part of the international jury of the 2021 Biennial of Illustration Bratislava.[4]