1) Monte Carlo does not have an airport so one would be looking at flying into Nice and then taking a bus or taxi to Monte Carlo!
2) The only operator out of Portugal serving Nice with direct flights is TAP - Air Portugal from Lisbon!
3) So, if it was me, I would scrap the Algarve leg. The Riviera will be much more interesting.
4) Fly into Lisbon, then to Nice, and then to Paris. or any combination thereof.
If scrapping the Algarve leg gives you a few more days, use it to explore the region North of Lisbon, even visiting Coimbra, Porto or the Douro valley. We can get April showers in the Algarve and going North may be more interesting.
5) For information the following airlines are currently reported as operating the following routes (January 2013):
Lisbon to Paris CDG
Easyjet
Air France
TAP - Air Portugal
Lisbon to Paris Orly
TAP - Air Portugal
Aigle Azur
Transavia (fm April 2013)
Lisbon to Nice
TAP - Air Portugal
Faro (Algarve) to Paris Orly
Easyjet
Aigle-Azur (fm April 2013)
Faro to Paris (Beauvais) (60 km north of Paris)
Ryanair
Paris to Paris CDG
Easyjet
Air France
TAP - Air Portugal
Porto to Paris (Orly)
TAP - Air Portugal
Aigle Azur
Transavia
Porto to Paris (Beauvais) (120 km north of Paris)
Ryanair
Porto to Paris (Vatry) (EuroDisney) (+-150 km north of Paris )
Ryanair
Trains between Portugal and France take +- 20 hours over night. I would recommend flying.
More info here: http://bit.ly/YwJLMA
In France, there is the excellent, but sometimes costly, TGV rail system operated by SNCF.
