If you pass the law with this event (option 1) :

# Regicide
# Triggered from enactment pulse
1848.1 = {
type = country_event
placement = root
title = 1848.1.t
desc = 1848.1.d
flavor = 1848.1.f

duration = 3

event_image = {
video = "gfx/event_pictures/europenorthamerica_springtime_of_nations.bk2"
}

on_created_soundeffect = "event:/SFX/UI/Alerts/event_appear"
on_opened_soundeffect = "event:/SFX/Events/europenorthamerica/springtime_of_nation"

icon = "gfx/interface/icons/event_icons/event_skull.dds"

trigger = {
has_law = law_type:law_monarchy
OR = {
is_enacting_law = law_type:law_presidential_republic
is_enacting_law = law_type:law_parliamentary_republic
}
any_interest_group = {
is_in_government = yes
leader = {
has_ideology = ideology_radical
}
}
NOT = {
has_modifier = regicide_averted
}
}

option = {
name = 1848.1.a
if = {
limit = {
is_enacting_law = law_type:law_presidential_republic
}
activate_law = law_type:law_presidential_republic
}
if = {
limit = {
is_enacting_law = law_type:law_parliamentary_republic
}
activate_law = law_type:law_parliamentary_republic
}
# monarchists get VERY angry
every_interest_group = {
limit = {
law_stance = {
law = law_type:law_monarchy
value > neutral
}
}
add_modifier = {
name = regicide
months = short_modifier_time
}
}
ruler = {
kill_character = yes
}
ai_chance = {
base = 25
}
}
option = {
name = 1848.1.b
default_option = yes
# gain success chance, lose enactment time
add_enactment_modifier = {
name = regicide_averted
}
ai_chance = {
base = 75
}
}
}

the event of the foundation of the seconde republic does not happen because the king and his son are kill and i'm pretty sure that block this trigger in your event chain

ruler = { has_variable = is_orleanist }