London and Paris on a High Speed Train
Once in the Heathrow Airport, at the information station, get a subway map and buy an Express train ticket to the Piccadilly Tube station. Note, there are cheaper transit options, or taxis, but I prefer speed and comfort when the price is reasonable. In the Piccadilly station, to go to the Eurostar high speed train, take the Hammersmith & City line to King's Cross station, the station made famous in the Harry Potter books. From King's Cross walk to St.Pancras to get the Eurostar.
Regarding Eurostar tickets, book a ticket online before going to the station. If you book well in advance, you may find sales. At the Eurostar station location, a helpful ticket master guided me as I printed my ticket. Then I queued up, went through security and immigration. With my France stamp in passport, I boarded the train and sat in my Preferred seat, no standard class for me today.
When entering the Chunnel, the under channel tunnel, there was no fan fare, no neon lights, just down into darkness for almost twenty minutes. It was a highlight for me because I had followed its construction in the science magazines; it was great human achievement. Then I was in France. Again the country side was placid and I fell asleep, waking as the train pulled into the station.
In France, I found a bank machine to get Euros, a subway map, a ticket machine, then I was on the subway to the museum.