Jules the Hedgehog's appearance in Sonic Underground would drastically alter the show's dynamics and plot. His presence, given his established character in the Archie comics, introduces several key changes:

1. Altered Family Dynamics: Jules's arrival would immediately impact the core family dynamic. While Sonic, Manic, and Sonia already have a strong bond, Jules's presence as their father would add a layer of complexity. The show might explore themes of parental reconciliation, dealing with past trauma (Jules's absence), and the challenges of reuniting a family after years of separation. His experience as a freedom fighter in Mobius could provide valuable strategic advice and combat skills to the Underground. The show could explore the differences in parenting styles between Queen Aleena and Jules, potentially leading to conflict or collaboration.

2. Enhanced Combat Capabilities: Jules, being a seasoned freedom fighter, would significantly bolster the Underground's fighting capabilities. His experience and skills would complement the siblings' abilities, providing tactical expertise and potentially introducing new fighting styles or techniques. He could train the siblings, improving their combat skills and strategic thinking. His presence would also make the Underground a more formidable force against Dr. Robotnik, potentially leading to earlier victories or different strategic approaches.

3. Political Intrigue and Alliances: Jules's connections and reputation in Mobius could introduce new political alliances and conflicts. His past experiences could provide insights into Robotnik's operations and weaknesses, leading to more effective strategies against him. He might have existing alliances with other freedom fighters or resistance groups, expanding the Underground's network and resources. This could also lead to new storylines involving political maneuvering and alliances against Robotnik's regime.

4. Exploration of Jules's Backstory: The show could delve deeper into Jules's past, exploring his experiences before his disappearance and the reasons behind his absence. This could provide flashbacks and backstory episodes, enriching the overall narrative and providing more context to his character. His relationship with Queen Aleena before and after his disappearance could be explored, adding emotional depth to the story.

5. Impact on Supporting Characters: The introduction of Jules would affect the relationships and roles of other characters. His presence might change the dynamics between the Underground and their allies, such as Snively or other resistance fighters. He could mentor or guide certain characters, influencing their development and actions throughout the series. The show could explore how Jules interacts with and influences characters like Uncle Chuck or other recurring allies.

6. New Story Arcs and Conflicts: Jules's arrival could open up entirely new story arcs and conflicts. He might have unresolved issues with old enemies or face new threats related to his past. His presence could attract the attention of Robotnik, leading to new and more challenging confrontations. The show could explore the consequences of his actions and the impact they have on the overall storyline.

In essence, Jules's inclusion would transform Sonic Underground from a story about a family rediscovering itself into a narrative about a family reuniting and fighting for freedom, with a seasoned freedom fighter leading the charge. The show's themes of family, freedom, and rebellion would be amplified, creating a richer and more complex storyline.